A371019 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x^3*exp(x)) ).

1, 0, 0, 6, 24, 60, 2280, 35490, 322896, 6532344, 175392720, 3351681630, 74021715240, 2328376978356, 68824597123464, 1989994550546730, 69687384248405280, 2634948077918611440, 98220733842576688416, 3966108617957749165494, 175679596523004500742840

Offset: 0

Author

Seiichi Manyama, Mar 08 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A161633, A371018.

Cf. A365287.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x^3*exp(x)))/x))

PARI

a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n+1, k)/(n-3*k)!)/(n+1);

Formula

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