A365893 Expansion of e.g.f. exp( Sum_{k>=0} x^(5*k+3) / (5*k+3)! ).

1, 0, 0, 1, 0, 0, 10, 0, 1, 280, 0, 165, 15400, 1, 30030, 1401400, 6995, 6806800, 190590401, 6506835, 1939938000, 36212380820, 4940624150, 687126039601, 9163671323015, 3761116975000, 297754623925175, 2982764271647875, 3067236941769001

Offset: 0

Author

Seiichi Manyama, Sep 22 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..613

Crossrefs

Cf. A006505, A009227, A307978.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(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-1,5*k+2) * a(n-5*k-3).