A365973 Expansion of e.g.f. exp( Sum_{k>=0} x^(4*k+3) / (4*k+3) ).

1, 0, 0, 2, 0, 0, 40, 720, 0, 2240, 172800, 3628800, 246400, 49420800, 3531340800, 87223136000, 18450432000, 3006222336000, 225434879488000, 6411312940032000, 2744461025280000, 435228787435520000, 35074217524469760000, 1126838040745697280000

Offset: 0

Author

Seiichi Manyama, Sep 23 2023

Keywords

• nonn

Crossrefs

Cf. A038205, A130915, A365974.

Cf. A365981.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\4, x^(4*k+3)/(4*k+3)))))

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-3)/4)} a(n-4*k-3)/(n-4*k-3)!.