A370985 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3*exp(x)) ).

1, 0, 0, 6, 24, 60, 3000, 45570, 403536, 10644984, 297562320, 5517833310, 142801022760, 5076208052916, 150282366476424, 4713707747551530, 189345734667052320, 7517503455423740400, 295622259241028433696, 13370535071068474177974, 642403497550155241197240

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A213644, A370984.

Cf. A358081, A370928.

Programs

PARI

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

PARI

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

Formula

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