A368587 a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+4,5) / k!.
0, 1, 4, 9, 20, 26, 96, -210, 2472, -20961, 211612, -2324729, 27901116, -362708320, 5077925048, -76168864092, 1218701840976, -20717931276243, 372922762998708, -7085532496941803, 141710649938878564, -2975923648716396714, 65470320271760793488
Offset: 0
Programs
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PARI
my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 4, binomial(4, k)*x^k/(k+1)!)*exp(x)/(1+x))))
Formula
a(0) = 0; a(n) = -n*a(n-1) + binomial(n+4,5).
E.g.f.: x * (1+2*x+x^2+x^3/6+x^4/120) * exp(x) / (1+x).