A365974 Expansion of e.g.f. exp( Sum_{k>=0} x^(5*k+3) / (5*k+3) ).

1, 0, 0, 2, 0, 0, 40, 0, 5040, 2240, 0, 1663200, 246400, 479001600, 605404800, 44844800, 699941088000, 274450176000, 355699625881600, 836634972096000, 156436600320000, 1437392253237248000, 1021561084051200000, 1124111547465274368000

Offset: 0

Author

Seiichi Manyama, Sep 23 2023

Keywords

• nonn

Crossrefs

Cf. A038205, A130915, A365973.

Cf. A365982.

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) = (n-1)! * Sum_{k=0..floor((n-3)/5)} a(n-5*k-3)/(n-5*k-3)!.