A365990 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(5*k+4) / (5*k+4) ).

1, 0, 0, 0, 6, 0, 0, 0, 2520, 40320, 0, 0, 7484400, 345945600, 6227020800, 0, 81729648000, 7410154752000, 307697854464000, 6402373705728000, 2375880867360000, 354798209525760000, 25460995321681920000, 1090665702016450560000, 26003493399464380800000

Offset: 0

Author

Seiichi Manyama, Sep 25 2023

Keywords

• nonn

Crossrefs

Cf. A365977, A365979, A365982.

Cf. A365914, A365989.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\5, x^(5*k+4)/(5*k+4)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-4)/5)} (5*k+3)! * binomial(n,5*k+4) * a(n-5*k-4).