A377391 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - x*log(1-x))^3 ).

1, 0, 6, 9, 528, 3150, 157032, 2060100, 102770112, 2276373456, 120136435200, 3868551141840, 221493499198848, 9438561453784320, 592954244405195904, 31417910131585330080, 2173884244961012121600, 137231093173511486016000, 10452538023125775799541760

Offset: 0

Author

Seiichi Manyama, Oct 27 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A371121, A377390.

Cf. A371231, A377361.

Programs

PARI

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

Formula

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A371231.

a(n) = 3 * n! * (3*n+2)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (3*n-k+3)! ).