%I #6 Mar 14 2024 09:01:53
%S 1,0,0,0,24,120,0,-2520,-20160,181440,3024000,19958400,-159667200,
%T -5708102400,-47221574400,326918592000,20748433305600,296406190080000,
%U -533531142144000,-126713646259200000,-3007337204551680000,-14688645874366464000,1183099972392898560000
%N Expansion of e.g.f. (1 + x^3 + x^4)^x.
%F a(n) = n! * Sum_{j=0..floor(n/3)} Sum_{k=0..j} binomial(j,n-3*j-k) * Stirling1(j,k)/j!.
%o (PARI) a(n) = n!*sum(j=0, n\3, sum(k=0, j, binomial(j, n-3*j-k)*stirling(j, k, 1)/j!));
%Y Cf. A371160.
%K sign
%O 0,5
%A _Seiichi Manyama_, Mar 14 2024
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