A380916 E.g.f. A(x) satisfies A(x) = exp(2 * x / (1 - x*A(x))) / (1 - x*A(x)).
1, 3, 20, 254, 4832, 123152, 3947008, 152638320, 6919663360, 359984690432, 21143150157824, 1384004213748224, 99919253031411712, 7887827865170055168, 675952599490594422784, 62495398874421426649088, 6200786173880446466785280, 657212589119205105944428544
Offset: 0
Keywords
Programs
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PARI
a(n, q=2, r=2, s=0, t=1, u=1/2) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);
Formula
a(n) = n! * Sum_{k=0..n} 2^k * (n-k+1)^(k-1) * binomial(2*n-k,n-k)/k!.