A365897 Expansion of e.g.f. exp( Sum_{k>=0} x^(3*k+5) / (3*k+5)! ).

1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 126, 1, 0, 1287, 1, 126126, 10803, 1, 5513508, 87210, 488864377, 175388031, 698820, 61841343565, 5037240879, 5194678451481, 5281277511511, 139251621015, 1519441856106345, 387880753064806, 123382468421090541

Offset: 0

Author

Seiichi Manyama, Sep 22 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..605

Crossrefs

Cf. A057814, A365896, A365898.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\3, x^(3*k+5)/(3*k+5)!))))

Formula

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