A378892 G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)^3).
1, 1, 5, 37, 322, 3067, 30951, 325171, 3519038, 38959997, 439177850, 5023590609, 58163050071, 680308820750, 8026782091957, 95419476630100, 1141762194395927, 13740910664096101, 166216043531507231, 2019807368837970964, 24644779751103948475, 301818330734940817283
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Keywords
Programs
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PARI
a(n, r=1, s=-1, t=6, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
Formula
G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^5/(1 + x*A(x)^3)).
If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(s*k,n-k)/(t*k+u*(n-k)+r).