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
Keywords
Programs
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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)!.