A377429 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-x))^4 ).

1, 4, 56, 1436, 54540, 2763696, 175688744, 13457185080, 1207241712536, 124205544781728, 14420516981211360, 1865347268407271040, 266056506383725529568, 41485848013549310521536, 7021170794004780911946048, 1281852242007649764308226240, 251124461130948243588667169280

Offset: 0

Author

Seiichi Manyama, Oct 28 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A052802, A376392, A376393.

Cf. A377426, A377427.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-x))^4)/x))

PARI

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

Formula

E.g.f. A(x) satisfies A(x) = 1/(1 + log(1 - x*A(x)))^4.

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377426.

a(n) = (4/(4*n+4)!) * Sum_{k=0..n} (4*n+k+3)! * |Stirling1(n,k)|.