A356811 a(n) = Sum_{k=0..n} (k*n+1)^(n-k) * binomial(n,k).
1, 2, 8, 71, 1040, 22457, 676000, 26861977, 1347932416, 82873789793, 6114540967424, 532596023373713, 53990083205042176, 6289985311473281329, 833180470332123750400, 124356049859476364116193, 20754548375601491155681280, 3847574240184742568296430273
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..274
Programs
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PARI
a(n) = sum(k=0, n, (k*n+1)^(n-k)*binomial(n, k));
Formula
a(n) = n! * [x^n] exp( x * (exp(n * x) + 1) ).
a(n) = [x^n] Sum_{k>=0} x^k / (1 - (n*k+1)*x)^(k+1).