A351281 - OEIS

%I #16 Feb 06 2022 11:03:28

%S 1,1,9,187,7173,440611,39631509,4910795107,802015652853,

%T 166948755155971,43146953460348309,13555255072473665827,

%U 5087595330217093070133,2248298922174973220446531,1155512971750307157457879509,683392198848998191062416885347

%N a(n) = Sum_{k=0..n} k! * k^k * Stirling2(n,k).

%F E.g.f.: Sum_{k>=0} (k * (exp(x) - 1))^k.

%F a(n) ~ exp(exp(-1)/2) * n! * n^n. - _Vaclav Kotesovec_, Feb 06 2022

%t a[0] = 1; a[n_] := Sum[k! * k^k * StirlingS2[n, k], {k, 1, n}]; Array[a, 16, 0] (* _Amiram Eldar_, Feb 06 2022 *)

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*(exp(x)-1))^k)))

%Y Cf. A000670, A122399, A229234, A282190, A350722, A351280.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 06 2022