A357664 Expansion of e.g.f. sinh( (exp(2*x) - 1)/sqrt(2) )/sqrt(2).

0, 1, 2, 6, 32, 220, 1592, 11944, 96000, 847120, 8209952, 86020704, 958326272, 11243157952, 138464594816, 1789358629504, 24250275913728, 344002396594432, 5092763802452480, 78443316497892864, 1253887341918199808, 20761127890765634560

Offset: 0

Author

Seiichi Manyama, Oct 07 2022

Keywords

• nonn

Crossrefs

Cf. A024429, A357665, A357666.

Cf. A009599, A264037, A357661.

Programs

PARI

my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sinh((exp(2*x)-1)/sqrt(2))/sqrt(2)))))

PARI

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

Formula

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