# Stirling number of the 2nd kind Calculator

## Calculates the Stirling number of the sevond kind S(n,k).

 n n=1,2,3,... k 1≦k≦n 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit S(n,k)
 $\normal Stirling\ number\ of\ the\ 2nd\ kind\ S(n,k)\\[10](1)\ {\large\sum_{\small k=0}^{\small n}}S(n,k)x(x-1)(x-2)\ldots (x-k+1)=x^n\\[10](2)\ S(n,0)={\large\delta}_{n0},\hspace{20}S(n,1)=S(n,n)=1\\[10]\hspace{25} S(n,k)=S(n-1,k-1)+kS(n-1,k),\\\hspace{240}1\le k\le n\\[10](3)\ S(n,k)={\large \frac{1}{k!} \sum_{\small j=0}^{\small k}}(-1)^{j}{}_{k}C_{j}(k-j)^n\\$

Stirling number of the 2nd kind
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