A382892 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^3 * A(x) )^3.
1, 3, 24, 190, 1659, 15309, 146986, 1453536, 14704917, 151479031, 1583533308, 16756882194, 179149227231, 1932144798513, 20996553430206, 229678298803028, 2527034248221849, 27947027713469307, 310494250880357488, 3463870813896354726, 38787008808135775299
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(s*k, n-k)/(t*k+u*(n-k)+r));
Formula
G.f. A(x) satisfies A(x) = ( 1 + x * (1+x)^3 * 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 A366272.