A367881 Expansion of e.g.f. 1/(1 - 3 * x * (exp(x) - 1)).
1, 0, 6, 9, 228, 1095, 23238, 215481, 4657992, 66216555, 1553967210, 29793656013, 777115661292, 18608934688383, 542832959656302, 15470567460571905, 503794462155308688, 16557037363336856019, 598704921471691072242, 22205328374455141122165
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\2, 3^k*k!*stirling(n-k, k, 2)/(n-k)!);
Formula
a(0) = 1; a(n) = 3 * n * Sum_{k=2..n} binomial(n-1,k-1) * a(n-k).
a(n) = n! * Sum_{k=0..floor(n/2)} 3^k * k! * Stirling2(n-k,k)/(n-k)!.