A375424 Expansion of e.g.f. exp(-x * (1 - x)) / (1 - x)^2.
1, 1, 5, 17, 101, 589, 4369, 35125, 323273, 3263129, 36301661, 439023001, 5748342445, 80949641317, 1220505157481, 19615065647549, 334764933094289, 6046684538094385, 115242737561241013, 2311256839666971169, 48658040610273601781, 1072909782649220737661
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x))/(1-x)^2)) -
PARI
a(n) = (-1)^n*n!*sum(k=0, n, binomial(k-2, n-k)/k!);
Formula
a(n) = (-1)^n * n! * Sum_{k=0..n} binomial(k-2,n-k)/k!.
a(n) = n*a(n-1) + 3*(n-1)*a(n-2) - 2*(n-1)*(n-2)*a(n-3).