A381016 Expansion of e.g.f. -log(1-x) * sin(x).

0, 0, 2, 3, 4, 20, 110, 651, 4520, 36000, 322618, 3213595, 35226860, 421419492, 5463436134, 76301056755, 1142009233872, 18236159031584, 309463272791538, 5561354285804115, 105510576441518164, 2107380222724155540, 44200537412519181278, 971311172969442165883

Offset: 0

Author

Seiichi Manyama, Feb 12 2025

Keywords

• nonn

Crossrefs

Cf. A002104, A009410, A009416, A177699.

Programs

PARI

my(N=30, x='x+O('x^N)); concat([0, 0], Vec(serlaplace(-log(1-x)*sin(x))))

PARI

a(n) = -sum(k=1, n\2, (-1)^k*(n-2*k)!*binomial(n, 2*k-1));

Formula

a(n) = -Sum_{k=1..floor(n/2)} (-1)^k * (n-2*k)! * binomial(n,2*k-1).