A376436 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^2*log(1-x))^2 ).

1, 0, 0, 12, 24, 80, 11160, 87696, 715680, 62337600, 1065980160, 15842534400, 1109943362880, 31591940440320, 731706348941568, 46767587926752000, 1889337264901632000, 61735665488234250240, 3896148715287564902400, 201584132714100384460800, 8661099107269708639948800, 567405718655558932535500800

Offset: 0

Author

Seiichi Manyama, Sep 22 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A376385, A376392.

Cf. A371235, A375639.

Programs

PARI

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

PARI

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

Formula

E.g.f. A(x) satisfies A(x) = 1/(1 + x^2*A(x)^2 * log(1 - x*A(x)))^2.

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371235.

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