A357665 Expansion of e.g.f. sinh( (exp(3*x) - 1)/sqrt(3) )/sqrt(3).

0, 1, 3, 12, 81, 765, 7938, 85239, 963819, 11801862, 158533443, 2320621569, 36425289816, 604576791405, 10532817901791, 192197187209484, 3673078679995677, 73486862051182425, 1536507360834633666, 33482575797899354235, 758209049155176114807

Offset: 0

Author

Seiichi Manyama, Oct 07 2022

Keywords

• nonn

Crossrefs

Cf. A024429, A357664, A357666.

Cf. A356572, A357572, A357662.

Programs

PARI

my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sinh((exp(3*x)-1)/sqrt(3))/sqrt(3)))))

PARI

a(n) = sum(k=0, (n-1)\2, 3^(n-1-k)*stirling(n, 2*k+1, 2));

Formula

a(n) = Sum_{k=0..floor((n-1)/2)} 3^(n-1-k) * Stirling2(n,2*k+1).