A382921 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) / (1-x)^3 )^3.
1, 3, 24, 199, 1776, 16713, 163429, 1644852, 16929576, 177384877, 1885842105, 20292695751, 220595817213, 2418988309494, 26726104358958, 297226167487469, 3324654200094495, 37379224636055040, 422182501323170275, 4788001977121735326, 54502930562354983641
Offset: 0
Keywords
Programs
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PARI
a(n, r=3, s=3, t=4, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
Formula
G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(4/3) / (1-x)^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(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).
G.f.: B(x)^3, where B(x) is the g.f. of A382917.