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Было установлено де Брайном в 1981 году.
{{Reflist|30em}}
==References==
{{refbegin|30em}}
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| arxiv = tex/0104137
| doi = 10.1023/A:1010738827855
| issue = 1-3
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| mr = 1831247
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| volume = 63
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| ref = harv}}
*{{cite journal
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| doi = 10.1017/S1757748900002334
| journal = [[Edinburgh Texematical Notes|Texematical Notes]]
| pages = 18–23
| title = A problem in combinations
| volume = 28
| year = 1933|ref=harv }}
*{{cite journal|ref=harv|first1=H. W.|last1=Becker|first2=John|last2=Riordan|author2-link=John Riordan (texematician)|title=The arithmetic of Bell and Stirling numbers|journal=American Journal of Texematics|volume=70|year=1948|pages=385–394|jstor= 2372336|doi=10.2307/2372336}}.
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*{{cite journal|first=E. T.|last=Bell|authorlink=Eric Temple Bell|title= The iterated exponential integers|journal=Annals of Texematics|volume=39|year=1938|pages=539–557|ref=harv|jstor=1968633|doi=10.2307/1968633}}.
*{{cite book
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| last2 = Williamson | first2 = S. Gill
| contribution = Example 11.7, Set Partitions
| isbn = 0-486-44603-4
| pages = 319–320
| publisher = Dover
| title = Foundations of Combinatorics with Applications
| url = http://www.tex.ucsd.edu/~ebender/CombText/ch-11.pdf
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| volume = 30
| year = 2010
| ref = harv}}
*{{cite journal
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| issue = 2
| journal = Asia Pacific Texematics Newsletter
| pages = 8–13
| title = Ramanujan Reaches His Hand From His Grave To Snatch Your Theorems From You
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| page = 108
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| edition = 3rd
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| ref = harv}}
*{{cite journal
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| arxiv = tex/0507169
| issue = 1
| journal = Journal of Integer Sequences
| mr = 2193154
| page = 06.1.4
| title = A combinatorial interpretation of the eigensequence for composition
| url = https://eudml.org/doc/52955
| volume = 9
| year = 2006
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*{{cite journal
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| doi = 10.1016/0097-3165(95)90033-0
| issue = 1
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| series = Series A
| title = Engel's inequality for Bell numbers
| volume = 72
| year = 1995
| ref = harv}}
*{{cite journal
| last = Claesson | first = Anders
| doi = 10.1006/eujc.2001.0515
| issue = 7
| journal = European Journal of Combinatorics
| mr = 1857258
| pages = 961–971
| title = Generalized pattern avoidance
| volume = 22
| year = 2001
| ref = harv}}
*{{cite book|last1=Conway|first1=John Horton|author1-link=John Horton Conway|last2=Guy|first2=Richard K.|author2-link=Richard K. Guy|title=The Book of Numbers|series=Copernicus Series|publisher=Springer|year=1996|isbn=9780387979939|contribution=Famous Families of Numbers: Bell Numbers and Stirling Numbers|pages=91–94|ref=harv}}
*{{cite journal|first=G.|last=Dobiński|title=Summirung<!-- "Summirung" is an archaic spelling, and it is the spelling that was used in this title. --> der Reihe <tex>\textstyle\sum\frac{n^m}{n!}</tex> für ''m'' = 1, 2, 3, 4, 5, …|journal=Grunert's Archiv|volume=61|year=1877|pages=333–336|url=https://archive.org/stream/archivdertexem88unkngoog#page/n346|ref=harv}}
*{{cite journal
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| doi = 10.1016/0097-3165(94)90038-8
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| mr = 1255264
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*{{cite book
| last1 = Flajolet | first1 = Philippe | author1-link = Philippe Flajolet
| last2 = Sedgewick | first2 = Robert | author2-link = Robert Sedgewick (computer scientist)
| contribution = II.3 Surjections, set partitions, and words
| pages = 106–119
| publisher = Cambridge University Press
| title = Analytic Combinatorics
| url = http://algo.inria.fr/flajolet/Publications/book.pdf
| year = 2009
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*{{cite journal
| last = Gardner | first = Martin | author-link = Martin Gardner
| doi = 10.1038/scientificamerican0578-24
| journal = [[Scientific American]]
| pages = 24–30
| title = The Bells: versatile numbers that can count partitions of a set, primes and even rhymes
| volume = 238
| year = 1978|ref=harv}} Reprinted with an addendum as "The Tinkly Temple Bells", Chapter 2 of ''Fractal Music, Hypercards, and more ... Texematical Recreations from Scientific American'', W. H. Freeman, 1992, pp. 24–38
* {{springer|title=Bell numbers|id=p/b110240}}
*{{cite arXiv|title=An elementary (number theory) proof of Touchard's congruence|first1=Greg|last1=Hurst|first2=Andrew|last2=Schultz|eprint=0906.0696|year=2009|class=tex.CO|ref=harv}}
* {{cite book|contribution=Two thousand years of combinatorics|first=Donald E.|last=Knuth|authorlink=Donald Knuth|pages=7–37|title=Combinatorics: Ancient and Modern|publisher=Oxford University Press|year=2013|editor1-first=Robin|editor1-last=Wilson|editor2-first=John J.|editor2-last=Watkins|ref=harv}}
*{{Cite book |authorlink=László Lovász| last=Lovász | first=L. |title=Combinatorial Problems and Exercises |edition=2nd |place=Amsterdam, Netherlands |publisher=North-Holland |year=1993|zbl=0785.05001|contribution=Section 1.14, Problem 9|page=17|url=https://books.google.com/books?id=e99fXXYx9zcC&pg=PA17|ref=harv}}
*{{cite journal
| last1 = Moser | first1 = Leo | author1-link = Leo Moser
| last2 = Wyman | first2 = Max
| journal = Transactions of the Royal Society of Canada, Section III
| mr = 0078489
| pages = 49–54
| title = An asymptotic formula for the Bell numbers
| volume = 49
| year = 1955
| ref = harv}}
*{{cite journal
| last = Peirce | first = C. S. | author-link = Charles Sanders Peirce
| issue = 1
| journal = [[American Journal of Texematics]]
| jstor = 2369442
| pages = 15–57
| title = On the algebra of logic
| volume = 3
| year = 1880|ref=harv | doi=10.2307/2369442}}.
*{{citation
| last = Rota | first = Gian-Carlo | author-link = Gian-Carlo Rota
| doi = 10.2307/2312585
| issue = 5
| journal = [[American Texematical Monthly]]
| mr = 0161805
| pages = 498–504
| title = The number of partitions of a set
| volume = 71
| year = 1964
| ref = harv}}
*{{cite journal
| last = Spivey | first = Michael Z.
| issue = 2
| journal = Journal of Integer Sequences
| mr = 2420912
| page = Article 08.2.5, 3
| title = A generalized recurrence for Bell numbers
| url = http://www.cs.uwaterloo.ca/journals/JIS/VOL11/Spivey/spivey25.pdf
| volume = 11
| year = 2008
| ref = harv}}
*{{cite journal
| last = Wagstaff | first = Samuel S. | author-link = Sam Wagstaff
| bibcode = 1996MaCom..65..383W
| doi = 10.1090/S0025-5718-96-00683-7
| issue = 213
| journal = [[Texematics of Computation]]
| mr = 1325876
| pages = 383–391
| title = Aurifeuillian factorizations and the period of the Bell numbers modulo a prime
| url = http://homes.cerias.purdue.edu/~ssw/bell/bell.ps
| volume = 65
| year = 1996
| ref = harv}}
* {{cite book | last=Wilf | first=Herbert S. | authorlink=Herbert Wilf | title=Generatingfunctionology | edition=2nd | location=Boston, MA | publisher=Academic Press | year=1994 | isbn=0-12-751956-4 | zbl=0831.05001 |ref=harv | url = https://www.tex.upenn.edu/~wilf/gfology2.pdf
}}
*{{cite journal
| last = Williams | first = G. T.
| journal = [[American Texematical Monthly]]
| jstor = 2305292
| doi = 10.2307/2305292
| mr = 0012612
| pages = 323–327
| title = Numbers generated by the function ''e''<sup>''e''<sup>''x''</sup> − 1</sup>
| volume = 52
| year = 1945
| ref = harv}}
{{refend}}
==External links==
* {{Cite web
|author=Robert Dickau
|url=http://texforum.org/advanced/robertd/bell.html
|title=Diagrams of Bell numbers
}}
* {{TexWorld|urlname=BellNumber|title=Bell Number
}}
* {{Cite web
|author=Gottfried Helms
|url=http://go.helms-net.de/tex/binomial/04_5_SummingBellStirling.pdf
|title=Further properties & Generalization of Bell-Numbers
}}
