A377582 Expansion of e.g.f. (1 + x * exp(x))^3.
1, 3, 12, 51, 228, 1035, 4698, 21063, 92424, 395091, 1643790, 6664383, 26387100, 102286587, 389125506, 1455994935, 5368721808, 19541252259, 70312410774, 250408115823, 883617559140, 3092276105163, 10740749281482, 37053754521831, 127037475064728, 433073722098675
Offset: 0
Programs
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PARI
a(n) = n!*sum(k=0, n, k^(n-k)*binomial(3, k)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(3,k)/(n-k)!.
G.f.: (1-17*x+127*x^2-542*x^3+1453*x^4-2543*x^5+2973*x^6-2478*x^7+1626*x^8-648*x^9) / ((1-x)^2*(1-2*x)^3*(1-3*x)^4).