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

%I #12 Dec 15 2023 09:10:27

%S 0,0,0,6,12,40,540,3528,25200,324000,3648960,41690880,622274400,

%T 9573033600,150465579264,2705877820800,51819600268800,

%U 1028013655818240,22086154437442560,504188626820659200,11997041025160396800,301999960230701322240

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

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

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

%Y Cf. A052804, A366777.

%Y Cf. A368165.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Dec 15 2023