A376387 Expansion of e.g.f. ( (1/x) * Series_Reversion( x*(1 + x*log(1-x))^3 ) )^(2/3).

1, 0, 4, 6, 376, 2220, 125028, 1614480, 92285856, 2018520000, 121850616240, 3907998135360, 253836993367296, 10891474747433280, 768302761361304960, 41447634607068318720, 3187906294983450762240, 206982374312337802536960, 17368877655215923728595968

Offset: 0

Author

Seiichi Manyama, Sep 22 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A371232, A376386.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1+x*log(1-x))^3)/x)^(2/3)))

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371232.

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