# Definition:Stirling's Triangle of the Second Kind

## Definition

Stirling's Triangle of the Second Kind is formed by arranging Stirling numbers of the second kind as follows:

$\begin{array}{r|rrrrrrrrrr} n & {n \brace 0} & {n \brace 1} & {n \brace 2} & {n \brace 3} & {n \brace 4} & {n \brace 5} & {n \brace 6} & {n \brace 7} & {n \brace 8} & {n \brace 9} \\ \hline 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 0 & 1 & 3 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 0 & 1 & 7 & 6 & 1 & 0 & 0 & 0 & 0 & 0 \\ 5 & 0 & 1 & 15 & 25 & 10 & 1 & 0 & 0 & 0 & 0 \\ 6 & 0 & 1 & 31 & 90 & 65 & 15 & 1 & 0 & 0 & 0 \\ 7 & 0 & 1 & 63 & 301 & 350 & 140 & 21 & 1 & 0 & 0 \\ 8 & 0 & 1 & 127 & 966 & 1701 & 1050 & 266 & 28 & 1 & 0 \\ 9 & 0 & 1 & 255 & 3025 & 7770 & 6951 & 2646 & 462 & 36 & 1 \\ \end{array}$

## Source of Name

This entry was named for James Stirling.