A370995 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^3*log(1-x)) ).

1, 0, 0, 0, 24, 60, 240, 1260, 209664, 2056320, 20476800, 221205600, 19370292480, 406935809280, 7376151444480, 131868581644800, 8376837844193280, 282378273124147200, 7891890567682867200, 207283550601631795200, 11520967360247698636800

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A052802, A370993, A370994.

Cf. A351504.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x^3*log(1-x)))/x))

PARI

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (n+k)! * |Stirling1(n-3*k,k)|/(n-3*k)!.