A375639 Expansion of e.g.f. 1 / (1 + x^2 * log(1 - x))^2.

1, 0, 0, 12, 24, 80, 2520, 17136, 124320, 2462400, 30965760, 372113280, 7014807360, 122840789760, 2078973921024, 43236813312000, 932206147891200, 20090534745415680, 480054835899371520, 12126262777282805760, 313198020852233932800

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A351503, A375679.

Cf. A375662.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[1/(1+x^2 Log[1-x])^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 29 2024 *)

PARI

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

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A351503.

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