A365972 Expansion of e.g.f. exp( Sum_{k>=0} x^(5*k+2) / (5*k+2) ).

1, 0, 1, 0, 3, 0, 15, 720, 105, 25920, 945, 712800, 39927195, 18532800, 4522138335, 486486000, 324696683025, 20936022307200, 19281559579425, 5026330152043200, 1045172736969075, 704618287875216000, 51145202778981886575, 76432873129004106000

Offset: 0

Author

Seiichi Manyama, Sep 23 2023

Keywords

• nonn

Crossrefs

Cf. A000166, A365971.

Cf. A365979.

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) = (n-1)! * Sum_{k=0..floor((n-2)/5)} a(n-5*k-2)/(n-5*k-2)!.