Stirling number of the 2nd kind Calculator

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

\(\normalsize Stirling\ number\ of\ the\ 2nd\ kind\ S(n,k)\\
(1)\ {\large\displaystyle \sum_{\small k=0}^{\small n}}S(n,k)x(x-1)(x-2)\ldots (x-k+1)=x^n\\
(2)\ S(n,0)={\large\delta}_{n0},\hspace{20px}S(n,1)=S(n,n)=1\\
\hspace{25px} S(n,k)=S(n-1,k-1)+kS(n-1,k),\\
\hspace{240px}1\le k\le n\\
(3)\ S(n,k)={\large \frac{1}{k!} \displaystyle \sum_{\small j=0}^{\small k}}(-1)^{j}{}_{k}C_{j}(k-j)^n\\
\)

Stirling number of the 2nd kind Calculator

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

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Stirling number of the 2nd kind Calculator

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

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