A370994 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^2*log(1-x)) ).

1, 0, 0, 6, 12, 40, 3060, 23688, 191520, 9698400, 158548320, 2304973440, 100716073920, 2627516361600, 58513944513024, 2512156283683200, 89046056086041600, 2739316757454950400, 124170651534918297600, 5440968468533003212800, 215067442349096186572800

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A052802, A370993, A370995.

Cf. A351503, A370989.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x^2*log(1-x)))/x))

PARI

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (n+k)! * |Stirling1(n-2*k,k)|/(n-2*k)!.