A370989 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2*(exp(x) - 1)) ).

1, 0, 0, 6, 12, 20, 2910, 22722, 117656, 8482392, 143398170, 1519998590, 79655138772, 2206506673956, 39101112995126, 1798446230741370, 68667380639283120, 1795441154500375472, 81344029377887798706, 3830461514154681289974, 135388937631209203030700

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A052894, A370988, A370990.

Cf. A358013.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2*(exp(x)-1)))/x))

PARI

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (n+k)! * Stirling2(n-2*k,k)/(n-2*k)!.