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Let $s(n,k)$ be a (signed) Stirling number of the first kind. Let $n \brace k$ be a Stirling number of the second kind. Let $$ f(n,m,i) = (-1)^{m-i+1}\sum\limits_{j=i}^{m+1}j^n s(j,i) {m+1 \brace j}...

Let $s(n,k)$ be a (signed) Stirling number of the first kind. Let $n \brace k$ be a Stirling number of the second kind. Let $a(n)$ be A329369 (i.e, number of permutations of ${1,2,...,m}$ with ...

Let $\left[{n \atop k}\right]$ be unsigned Stirling numbers of the first kind. Here $$ \left[{n \atop k}\right] = (n-1)\left[{n-1 \atop k}\right] + \left[{n-1 \atop k-1}\right], \\ \left[{n \atop 0}\...