A383382 Expansion of e.g.f. exp(-3*x) / (1-x)^5.
1, 2, 9, 48, 321, 2502, 22329, 223668, 2481921, 30187242, 399071529, 5694475608, 87197543361, 1425766728942, 24787205125209, 456477484618908, 8875541469155841, 181670665706512722, 3904395263350689609, 87898121215165479168, 2068411075529464370241, 50778930934558144895382
Offset: 0
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-3*x)/(1-x)^5))
Formula
a(n) = n! * Sum_{k=0..n} (-3)^(n-k) * binomial(k+4,4)/(n-k)!.
a(0) = 1, a(1) = 2; a(n) = (n+1)*a(n-1) + 3*(n-1)*a(n-2).
a(n) ~ sqrt(2*Pi) * n^(n + 9/2) / (24*exp(n+3)). - Vaclav Kotesovec, Apr 25 2025