A367875 Expansion of e.g.f. exp(x * (3 + exp(x))).
1, 4, 18, 91, 512, 3169, 21352, 155257, 1209680, 10039825, 88318136, 819958033, 8004898600, 81913041721, 876117919616, 9770201709649, 113347591376672, 1365288066794017, 17043527322085096, 220145837754233713, 2937871757773069496, 40451715334029650953
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n, (k+3)^(n-k)*binomial(n, k));
Formula
G.f.: Sum_{k>=0} x^k / (1 - (k+3)*x)^(k+1).
a(n) = Sum_{k=0..n} (k+3)^(n-k) * binomial(n,k).
a(0) = 1; a(n) = 3 * a(n-1) + Sum_{k=1..n} binomial(n-1,k-1) * k * a(n-k). - Ilya Gutkovskiy, Feb 02 2024