A365129 G.f. satisfies A(x) = (1 + x*A(x)*(1 + x*A(x))^2)^2.
1, 2, 9, 44, 240, 1386, 8346, 51802, 329086, 2129330, 13984095, 92974510, 624568680, 4232731050, 28904102829, 198688337014, 1373763563150, 9547516671684, 66660156446189, 467342635522698, 3288691828900768, 23220922841177476, 164465227646878689
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, t=2) = sum(k=0, n, binomial(t*(n+1), k)*binomial(s*k, n-k))/(n+1);
Formula
If g.f. satisfies A(x) = (1 + x*A(x)*(1 + x*A(x))^s)^t, then a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(t*(n+1),k) * binomial(s*k,n-k).