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

%I #19 Sep 29 2024 13:50:39

%S 1,0,0,12,24,80,2520,17136,124320,2462400,30965760,372113280,

%T 7014807360,122840789760,2078973921024,43236813312000,932206147891200,

%U 20090534745415680,480054835899371520,12126262777282805760,313198020852233932800

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

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

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

%t 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 *)

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

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

%Y Cf. A351503, A375679.

%Y Cf. A375662.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Aug 23 2024