A365419 Expansion of e.g.f. exp( Sum_{k>=0} x^(5*k+2) / (5*k+2)! ).

1, 0, 1, 0, 3, 0, 15, 1, 105, 36, 945, 990, 10396, 25740, 136942, 675675, 2238405, 18378361, 50490765, 523833819, 1665638325, 15790609395, 71976549646, 515107015830, 3524757498023, 19222751356875, 181500385651325, 888496839591076, 9603885700913400

Offset: 0

Author

Seiichi Manyama, Sep 22 2023

Keywords

• nonn

Crossrefs

Cf. A000296, A365338.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\5, x^(5*k+2)/(5*k+2)!))))

Formula

a(0)=1; a(n) = Sum_{k=0..floor((n-2)/5)} binomial(n-1,5*k+1) * a(n-5*k-2).