A367874 Expansion of e.g.f. exp(x * (2 + exp(x))).
1, 3, 11, 48, 241, 1358, 8445, 57256, 419233, 3290202, 27507349, 243731084, 2278919697, 22402234390, 230781192301, 2484462888312, 27880896280513, 325432611292082, 3943062342781605, 49504837209940612, 642982531293731761, 8626753575445207278
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n, (k+2)^(n-k)*binomial(n, k));
Formula
G.f.: Sum_{k>=0} x^k / (1 - (k+2)*x)^(k+1).
a(n) = Sum_{k=0..n} (k+2)^(n-k) * binomial(n,k).
a(0) = 1; a(n) = 2 * a(n-1) + Sum_{k=1..n} binomial(n-1,k-1) * k * a(n-k). - Ilya Gutkovskiy, Feb 02 2024