A380720 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2 * (1 - x*A(x))^4) / (1 - x*A(x))^2.
1, 3, 27, 427, 9829, 299421, 11399767, 522120299, 27993612745, 1721382881401, 119487832998811, 9244561661068647, 788985451618181869, 73644131873399817653, 7463589265871298367711, 816231439143125763495811, 95811879190166378655829393, 12015708296507465444922873585
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (n+k+1)^(k-1)*binomial(3*n-3*k+1, n-k)/k!);
Formula
a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(3*n-3*k+1,n-k)/k!.