A383383 Expansion of e.g.f. exp(-4*x) / (1-x)^5.
1, 1, 6, 26, 176, 1296, 11296, 110176, 1197696, 14304896, 186166016, 2620022016, 39631568896, 640971452416, 11034441916416, 201411030081536, 3884642996289536, 78929236862140416, 1684881987266215936, 37695662812132212736, 881964287274876665856, 21536903057742987001856
Offset: 0
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-4*x)/(1-x)^5))
Formula
a(n) = n! * Sum_{k=0..n} (-4)^(n-k) * binomial(k+4,4)/(n-k)!.
a(0) = a(1) = 1; a(n) = n*a(n-1) + 4*(n-1)*a(n-2).
a(n) = A383344(n+2)/(4*(n+1)).
a(n) ~ sqrt(2*Pi) * n^(n + 9/2) / (24*exp(n+4)). - Vaclav Kotesovec, Apr 25 2025