A370997 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^3/6*log(1-x)) ).

1, 0, 0, 0, 4, 10, 40, 210, 6944, 65520, 640800, 6837600, 157375680, 2741618880, 45897895680, 783559576800, 18503310228480, 440531086195200, 10407471103411200, 247739364392083200, 6801330820818124800, 198670207398879283200, 5945924796494183424000

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370993, A370996.

Cf. A351506.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x^3/6*log(1-x)))/x))

PARI

a(n) = sum(k=0, n\4, (n+k)!*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (n+k)! * |Stirling1(n-3*k,k)|/(6^k * (n-3*k)!).