A380764 E.g.f. A(x) satisfies A(x) = exp(x * (1 - x*A(x))) / (1 - x*A(x))^2.
1, 3, 21, 283, 5825, 161281, 5616415, 235957275, 11619036385, 656499970657, 41874164431631, 2976512157543739, 233338979438666161, 20000563338051696609, 1860931002481238778511, 186799953169800497128891, 20122315691834196706830017, 2315417027513322899728489537
Offset: 0
Keywords
Programs
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PARI
a(n, q=1, r=1, s=0, t=-1, 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-4*k+1,n-k)/k!.