A367284 G.f. satisfies A(x) = 1 + x*A(x) * (1 + x*A(x)^3)^3.
1, 1, 4, 19, 107, 648, 4144, 27500, 187654, 1308361, 9280049, 66749995, 485741501, 3569653591, 26454406231, 197482954338, 1483619134872, 11208536870979, 85101381927454, 649017399223259, 4969510058193925, 38189305411228229, 294440263583908772
Offset: 0
Keywords
Programs
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PARI
a(n, s=3, t=1, u=3) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+1));
Formula
If g.f. satisfies A(x) = 1 + x*A(x)^t * (1 + x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(s*k,n-k) / (t*k+u*(n-k)+1).