A380606 Expansion of e.g.f. exp(3*x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
1, 3, 27, 459, 11817, 411183, 18090459, 963856071, 60351513777, 4344290172891, 353515902334299, 32093341598006307, 3215888732193019353, 352572962113533923271, 41981774097966848444763, 5395346708265250105968927, 744369113570455426540767201, 109733083289828610273889269939
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, 3*n!*sum(k=0, n-1, 3^(n-k)*binomial(3*n+k, k)/((3*n+k)*(n-k-1)!)));
Formula
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A380515.
a(n) = 3 * n! * Sum_{k=0..n-1} 3^(n-k) * binomial(3*n+k,k)/((3*n+k) * (n-k-1)!) for n > 0.