A380914 E.g.f. A(x) satisfies A(x) = exp(x / (1 - x*A(x))) / (1 - x*A(x)).
1, 2, 11, 115, 1797, 37621, 990313, 31452905, 1171010809, 50029903081, 2413119476781, 129719605920565, 7690829719605541, 498579900892422077, 35086898369381747281, 2663953520081549084401, 217057092837921132411249, 18892120969438125131207377, 1749385548844357561820688853
Offset: 0
Keywords
Programs
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PARI
a(n, q=1, r=1, 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} (n-k+1)^(k-1) * binomial(2*n-k,n-k)/k!.