A375630 Expansion of e.g.f. exp(2*x) / (1 - x^3 * exp(x)).
1, 2, 4, 14, 88, 572, 4024, 37298, 404464, 4601528, 58426864, 846080798, 13209174136, 219868220756, 3981563464792, 77708414601098, 1606665377716576, 35246223612156272, 821962294211430496, 20227931586257247542, 522932344617513862696, 14204133017700173041292
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^3*exp(x)))) -
PARI
a(n) = n!*sum(k=0, n\3, (k+2)^(n-3*k)/(n-3*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} (k+2)^(n-3*k)/(n-3*k)!.