A365155 G.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x))^2 )^2.
1, 2, 13, 98, 838, 7690, 74047, 738028, 7549658, 78811732, 836219773, 8991739874, 97769604542, 1073156173442, 11875174074608, 132333387616600, 1483789788291516, 16727705523572128, 189496296040063170, 2155984626357225948, 24625450759174328948
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, t=2) = sum(k=0, n, binomial(t*(n+k+1), k)*binomial(s*k, n-k)/(n+k+1));
Formula
If g.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x))^s )^t, then a(n) = Sum_{k=0..n} binomial(t*(n+k+1),k) * binomial(s*k,n-k)/(n+k+1).