A380917 E.g.f. A(x) satisfies A(x) = exp(3 * x / (1 - x*A(x))) / (1 - x*A(x)).
1, 4, 31, 453, 9957, 293103, 10850625, 484699491, 25381819737, 1525299702363, 103484966417109, 7824985701013143, 652582573442231733, 59509330659228595239, 5890961096785803165129, 629159786981753244521787, 72111288184913038638092337, 8828896697592792281849882547
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Keywords
Programs
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PARI
a(n, q=3, r=3, s=0, t=1, u=1/3) = 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} 3^k * (n-k+1)^(k-1) * binomial(2*n-k,n-k)/k!.