A365917 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(4*k+5) / (4*k+5)! ).

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 252, 0, 0, 1, 4004, 756756, 0, 1, 65756, 69837768, 11732745024, 1, 1047508, 5772957036, 3957845988096, 623360743125121, 16781260, 475191562560, 1078063276530240, 587517500395425601, 88832646060056769732, 38604505286340

Offset: 0

Author

Seiichi Manyama, Sep 23 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A245790, A365915, A365916.

Cf. A352429, A365911.

Cf. A365898.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1+x-(sinh(x)+sin(x))/2)))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-5)/4)} binomial(n,4*k+5) * a(n-4*k-5).

E.g.f.: 1 / ( 1 + x - (sinh(x) + sin(x))/2 ).