A382885 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x) * A(x) )^3.
1, 3, 18, 121, 900, 7110, 58598, 498153, 4336533, 38463732, 346368351, 3158325168, 29102914959, 270582713670, 2535191045652, 23913087584045, 226892934532149, 2164080724942155, 20737076963936828, 199542537271568802, 1927347504059464995, 18679645863925666721
Offset: 0
Keywords
Programs
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PARI
a(n, r=3, s=1, t=4, u=0) = 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 + x * (1+x) * A(x)^(4/3) )^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).
G.f.: B(x)^3, where B(x) is the g.f. of A365178.