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Expansion of e.g.f. (1 - x * log(1 - x))^4.
2

%I #10 Nov 04 2024 09:08:52

%S 1,0,8,12,176,840,7416,58800,529728,5152896,54070560,612342720,

%T 7472424384,97979207040,1375839795456,20619488373120,328716465177600,

%U 5556948993792000,99324048442208256,1871986425192990720,37110785352536724480,772059856808638218240,16820447458491885035520

%N Expansion of e.g.f. (1 - x * log(1 - x))^4.

%F a(n) = n! * Sum_{k=0..floor(n/2)} k! * binomial(4,k) * |Stirling1(n-k,k)|/(n-k)!.

%o (PARI) a(n) = n!*sum(k=0, n\2, k!*binomial(4, k)*abs(stirling(n-k, k, 1))/(n-k)!);

%Y Cf. A377682, A377683.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Nov 04 2024