A365982 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(5*k+3) / (5*k+3) ).

1, 0, 0, 2, 0, 0, 80, 0, 5040, 13440, 0, 3326400, 5913600, 479001600, 3632428800, 5381376000, 1399882176000, 6586804224000, 364469833728000, 5019809832576000, 18772392038400000, 2898136435138560000, 24517466017228800000, 1203790902897623040000

Offset: 0

Author

Seiichi Manyama, Sep 24 2023

Keywords

• nonn

Crossrefs

Cf. A355284, A365980, A365981.

Cf. A365912, A365974.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\5, x^(5*k+3)/(5*k+3)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-3)/5)} (5*k+2)! * binomial(n,5*k+3) * a(n-5*k-3).