First-kind Stirling number
Calculates the first-kind Stirling number s(n, k).
| s(n,k) |
| \(\normalsize Stirling\ number\ of\ the\ 1st\ kind\ s(n,k)\\ (1)\ x(x-1)(x-2)\ldots (x-n+1)={\large\displaystyle \sum_{\small k=0}^{\small n}}s(n,k)x^k\\ (2)\ s(n,0)={\large\delta}_{n0},\hspace{20px}s(n,n)=1\\ \hspace{25px} s(n,k)=s(n-1,k-1)-(n-1)s(n-1,k),\\ \hspace{240px}1\le k\le n\\ \) |
No customer feedback for this calculation yet.