A353287 a(n) = Sum_{k=0..floor(n/2)} k^k * Stirling2(n-k,k).

1, 0, 1, 1, 5, 13, 56, 223, 1056, 5243, 28401, 163578, 1003332, 6506149, 44464510, 319066188, 2396942740, 18800878491, 153611297283, 1304600660023, 11495292868763, 104907727533628, 990067627794487, 9648859125705064, 96978616443859923

Offset: 0

Author

Seiichi Manyama, Apr 09 2022

Keywords

• nonn

Crossrefs

Cf. A097341, A097342, A171367, A353260, A353261.

Cf. A353288.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, k^k*x^(2*k)/prod(j=1, k, 1-j*x)))

PARI

a(n) = sum(k=0, n\2, k^k*stirling(n-k, k, 2));

Formula

G.f.: Sum_{k>=0} k^k * x^(2*k)/Product_{j=1..k} (1 - j * x).