A376386 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x))^3 ).

1, 0, 6, 9, 600, 3510, 204372, 2617020, 152727936, 3319236144, 203151929040, 6485780434320, 425284393933440, 18190896271479360, 1291781802823916544, 69545182272420909600, 5374429456543444177920, 348502600060029871948800, 29344904433432469953368064

Offset: 0

Author

Seiichi Manyama, Sep 22 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370993, A376385.

Cf. A371232, A376387.

Cf. A375672.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x))^3)/x))

PARI

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

Formula

E.g.f. A(x) satisfies A(x) = 1/(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 A371232.

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