A380605 Expansion of e.g.f. exp(2*x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
1, 2, 16, 260, 6544, 224672, 9797824, 518778752, 32332764160, 2319086302208, 188178044545024, 17043816700333568, 1704575787500099584, 186577340672207974400, 22185432394552519868416, 2847773562263558405439488, 392481896442656581445287936, 57805399208817471918851883008
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, 3*n!*sum(k=0, n-1, 2^(n-k)*binomial(3*n+k, k)/((3*n+k)*(n-k-1)!)));
Formula
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380515.
a(n) = 3 * n! * Sum_{k=0..n-1} 2^(n-k) * binomial(3*n+k,k)/((3*n+k) * (n-k-1)!) for n > 0.