A376394 Expansion of e.g.f. ( (1/x) * Series_Reversion( x*(1 + log(1-x))^3 ) )^(2/3).

1, 2, 20, 388, 11382, 449868, 22427988, 1351746912, 95626268208, 7769995319280, 713229439560816, 73000860715645344, 8243857485642410400, 1018250616169754862048, 136561871538665054975520, 19763248903874313555142656, 3069876028020976768409255808, 509447295061343606934940250880

Offset: 0

Author

Seiichi Manyama, Sep 22 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A367139, A376393.

Programs

PARI

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

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367139.

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