A365976 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(4*k+1) / (4*k+1) ).

1, 1, 2, 6, 24, 144, 1008, 8064, 72576, 766080, 8934912, 113895936, 1573254144, 23864924160, 389247344640, 6786673496064, 125855767166976, 2492616008171520, 52243870155079680, 1154797100239749120, 26835102086208159744, 656159502089355264000

Offset: 0

Author

Seiichi Manyama, Sep 23 2023

Keywords

• nonn

Crossrefs

Cf. A296676, A365975, A365977.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\4, x^(4*k+1)/(4*k+1)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} (4*k)! * binomial(n,4*k+1) * a(n-4*k-1).