A380769 E.g.f. A(x) satisfies A(x) = exp(x / (1 - x*A(x)^2)) / (1 - x*A(x)^2).
1, 2, 15, 244, 6097, 206806, 8882599, 462280960, 28279981825, 1989026203114, 158149907916031, 14028441592927180, 1373477000345414353, 147124479131269256254, 17115976784139798114775, 2149092237059821309705816, 289673905062350873773963393, 41719133895880374350508378322
Offset: 0
Keywords
Programs
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PARI
a(n, q=1, r=2, s=0, t=1, u=1) = 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*n-2*k+1)^(k-1) * binomial(3*n-2*k,n-k)/k!.