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%I #14 Sep 01 2022 09:31:08
%S 1,2,8,71,1040,22457,676000,26861977,1347932416,82873789793,
%T 6114540967424,532596023373713,53990083205042176,6289985311473281329,
%U 833180470332123750400,124356049859476364116193,20754548375601491155681280,3847574240184742568296430273
%N a(n) = Sum_{k=0..n} (k*n+1)^(n-k) * binomial(n,k).
%H Seiichi Manyama, <a href="/A356811/b356811.txt">Table of n, a(n) for n = 0..274</a>
%F a(n) = n! * [x^n] exp( x * (exp(n * x) + 1) ).
%F a(n) = [x^n] Sum_{k>=0} x^k / (1 - (n*k+1)*x)^(k+1).
%o (PARI) a(n) = sum(k=0, n, (k*n+1)^(n-k)*binomial(n, k));
%Y Cf. A080108, A240165, A245834.
%Y Cf. A356806, A356814, A356817.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Aug 29 2022
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