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%I #8 Nov 04 2024 09:15:18
%S 1,0,6,9,84,375,1998,11361,60840,299403,1368930,5906373,24362748,
%T 97019247,375712470,1422455625,5286155088,19340722707,69831127242,
%U 249265052301,880927979940,3086000399223,10726216043070,37020328044945,126961071656184,432900077950875
%N Expansion of e.g.f. (1 + x * (exp(x) - 1))^3.
%F a(n) = n! * Sum_{k=0..floor(n/2)} k! * binomial(3,k) * Stirling2(n-k,k)/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, k!*binomial(3, k)*stirling(n-k, k, 2)/(n-k)!);
%Y Cf. A377646, A377681.
%Y Cf. A375661.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Nov 04 2024