A356806 - OEIS

%I #18 Sep 01 2022 09:31:30

%S 1,0,4,27,448,10625,344736,14437213,753991680,47974773393,

%T 3650824000000,326917384798301,33956137832546304,4041303651931462969,

%U 545552768347831566336,82828479894303251953125,14040577418634835164921856,2640293357854435329683551265

%N a(n) = Sum_{k=0..n} (k*n-1)^(n-k) * binomial(n,k).

%H Seiichi Manyama, <a href="/A356806/b356806.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) = n! * Sum_{k=0..floor(n/2)} n^(n-k) * Stirling2(n-k,k)/(n-k)!.

%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));

%o (PARI) a(n) = n!*sum(k=0, n\2, n^(n-k)*stirling(n-k, k, 2)/(n-k)!);

%Y Cf. A052506, A351736, A351737.

%Y Cf. A356811, A356814, A356817.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 29 2022