A370996 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^2/2*log(1-x)) ).

1, 0, 0, 3, 6, 20, 810, 6174, 49560, 1439640, 22060080, 312487560, 8687891520, 199853503200, 4216976539776, 126706600944000, 3771722349158400, 106462579493088000, 3626324277349651200, 129806833608095575680, 4565069619653632320000

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370993, A370997.

Cf. A351505.

Programs

PARI

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

PARI

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

Formula

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