A377393 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*(exp(x) - 1))^3 ).

1, 0, 6, 9, 516, 3075, 149418, 1956171, 95139432, 2099836899, 108189172830, 3465051871083, 194015893087404, 8207832658120563, 505114926236953074, 26525536061251639275, 1800555184934893332048, 112493970299385975997635, 8415880480577316204054630

Offset: 0

Author

Seiichi Manyama, Oct 27 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A371119, A377392.

Cf. A371272.

Programs

PARI

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

Formula

E.g.f. satisfies A(x) = ( 1 + x*A(x) * (exp(x*A(x)) - 1) )^3.

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A371272.

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