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<!-- КРОВЬКИШКИТЕХ -->
<tex dpi = "150">x^{k} = x\sum_{i=0}^{k-1} \textstyle \lbrace{k-1\atop i}\rbrace x^{\underline{i}} = \sum_{i=0}^{k-1} \textstyle \lbrace{k-1\atop i}\rbrace x^{\underline{i}}(x-i+i) = \sum_{i=0}^{k-1} \textstyle \lbrace{k-1\atop i}\rbrace (x^{\underline{i+1}}+ix^{\underline{i}}) = \sum_{i=0}^k \textstyle \lbrace{k-1\atop i-1}\rbrace x^{\underline{i}}+\sum_{i=0}^k \textstyle \lbrace{k-1\atop i}\rbrace ix^{\underline{i}} = \sum_{i=0}^k (\textstyle \lbrace{k-1\atop i-1}\rbrace + i\textstyle \lbrace{k-1\atop i}\rbrace)x^{\underline{i}} = \sum_{i=0}^k \textstyle \lbrace{k\atop i}\rbrace x^{\underline{i}}</tex>
=== Таблица значений ===
!0
|1
|0 |0 |0 |0 |0 |0 |0 |0 |0
|-
!1
|0
|1
|0 |0 |0 |0 |0 |0 |0 |0
|-
!2
|1
|1
|0 |0 |0 |0 |0 |0 |0
|-
!3
|3
|1
|0 |0 |0 |0 |0 |0
|-
!4
|6
|1
|0 |0 |0 |0 |0
|-
!5
|10
|1
|0 |0 |0 |0
|-
!6
|15
|1
|0 |0 |0
|-
!7
|21
|1
|0 |0
|-
!8
|28
|1
|0
|-
!9
