A380768 E.g.f. A(x) satisfies A(x) = exp(x * A(x) / (1 - x*A(x)^2)) / (1 - x*A(x)^2).
1, 2, 19, 361, 10481, 411961, 20477185, 1232420449, 87148819441, 7083132622561, 650681345267801, 66674532650884753, 7540078499903430937, 932840158873518067537, 125332464410926005144241, 18173310946391976757487041, 2828702590649296770695135585, 470432341506749952275419504321
Offset: 0
Keywords
Programs
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PARI
a(n, q=1, r=2, s=1, 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-k+1)^(k-1) * binomial(3*n-k,n-k)/k!.