A365912 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(5*k+3) / (5*k+3)! ).

1, 0, 0, 1, 0, 0, 20, 0, 1, 1680, 0, 330, 369600, 1, 180180, 168168000, 13990, 163363200, 137225088001, 39041010, 232792560000, 182509367449640, 118574979600, 494730748512001, 369398970833730090, 451334037000000, 1500683270499930350, 1080492079984609149000

Offset: 0

Author

Seiichi Manyama, Sep 22 2023

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..498

Crossrefs

Cf. A102233, A332258, A365911.

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)} binomial(n,5*k+3) * a(n-5*k-3).