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A375639
Expansion of e.g.f. 1 / (1 + x^2 * log(1 - x))^2.
2
1, 0, 0, 12, 24, 80, 2520, 17136, 124320, 2462400, 30965760, 372113280, 7014807360, 122840789760, 2078973921024, 43236813312000, 932206147891200, 20090534745415680, 480054835899371520, 12126262777282805760, 313198020852233932800
OFFSET
0,4
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)!.
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 *)
PROG
(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)!);
CROSSREFS
Cf. A375662.
Sequence in context: A081751 A120360 A120356 * A376436 A109745 A364726
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 23 2024
STATUS
approved