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Expansion of e.g.f. -log(1 - x^3 * (exp(x) - 1)).
1

%I #11 Dec 15 2023 09:10:15

%S 0,0,0,0,24,60,120,210,20496,181944,1059120,4990590,180292200,

%T 3191349876,36598884504,327837512730,7732754793120,194896185648240,

%U 3574721299186656,51311061420097014,1105883184455171640,32127696556638165420,812811279492629700360

%N Expansion of e.g.f. -log(1 - x^3 * (exp(x) - 1)).

%F a(n) = n! * Sum_{k=1..floor(n/4)} (k-1)! * Stirling2(n-3*k,k)/(n-3*k)!.

%o (PARI) a(n) = n!*sum(k=1, n\4, (k-1)!*stirling(n-3*k, k, 2)/(n-3*k)!);

%Y Cf. A052858, A366564.

%Y Cf. A368174.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Dec 15 2023