A358013 Expansion of e.g.f. 1/(1 - x^2 * (exp(x) - 1)).
1, 0, 0, 6, 12, 20, 750, 5082, 23576, 453672, 5755770, 50894030, 841270452, 14694142476, 201442729670, 3552604015170, 73814245552560, 1369932831933392, 27860865121662066, 655240785723048726, 15052226249248287500, 357713461766745539700, 9416426612423343023742
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^2*(exp(x)-1)))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=3, i, 1/(j-2)!*v[i-j+1]/(i-j)!)); v;
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PARI
a(n) = n!*sum(k=0, n\3, k!*stirling(n-2*k, k, 2)/(n-2*k)!);
Formula
a(0) = 1; a(n) = n! * Sum_{k=3..n} 1/(k-2)! * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/3)} k! * Stirling2(n-2*k,k)/(n-2*k)!.