A365156 G.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x))^2 )^3.
1, 3, 27, 295, 3648, 48513, 677450, 9797031, 145458252, 2204380144, 33960095667, 530268482913, 8373331428836, 133484219528982, 2145376940485452, 34725549386905863, 565567039020594492, 9261756210015412356, 152410211630410153468
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, t=3) = 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).