A361638 Expansion of g.f. A(x) satisfying A(x) = 1 + x * A(x)^2 * (1 + A(x)^3).
1, 2, 14, 142, 1690, 21994, 303126, 4348102, 64235570, 970695442, 14934154334, 233133082494, 3683546302538, 58794776161274, 946619511627622, 15355445768326710, 250717346336174690, 4117189670041072930, 67956239699290313646, 1126763233375565370990
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n, binomial(n, k)*binomial(2*n+3*k+1, n)/(2*n+3*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(2*n+3*k+1,n)/(2*n+3*k+1).