A370990 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3*(exp(x) - 1)) ).

1, 0, 0, 0, 24, 60, 120, 210, 201936, 1996344, 12701520, 64865790, 17053788840, 374788816116, 4944496679304, 50034166184730, 6390396135006240, 239770550508132720, 5363062998193560096, 89908444484550625014, 7402557588108228698040

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A052894, A370988, A370989.

Cf. A358014.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\4, (n+k)!*stirling(n-3*k, k, 2)/(n-3*k)!)/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (n+k)! * Stirling2(n-3*k,k)/(n-3*k)!.