A380765 E.g.f. A(x) satisfies A(x) = exp(x * (1 - x*A(x))^2) / (1 - x*A(x))^2.
1, 3, 19, 241, 4853, 131601, 4466875, 182546421, 8739580841, 480023587297, 29759608788551, 2055884656223949, 156623317577663293, 13045653418406432721, 1179479817324874518419, 115042876530398843323621, 12041278143223263581774417, 1346252625757920938545507521
Offset: 0
Keywords
Programs
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PARI
a(n, q=1, r=1, s=0, t=-2, u=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} (n-k+1)^(k-1) * binomial(3*n-5*k+1,n-k)/k!.