A377680 Expansion of e.g.f. (1 + x * (exp(x) - 1))^3.
1, 0, 6, 9, 84, 375, 1998, 11361, 60840, 299403, 1368930, 5906373, 24362748, 97019247, 375712470, 1422455625, 5286155088, 19340722707, 69831127242, 249265052301, 880927979940, 3086000399223, 10726216043070, 37020328044945, 126961071656184, 432900077950875
Offset: 0
Programs
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PARI
a(n) = n!*sum(k=0, n\2, k!*binomial(3, k)*stirling(n-k, k, 2)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} k! * binomial(3,k) * Stirling2(n-k,k)/(n-k)!.