A382919 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) / (1-x)^3 )^2.
1, 2, 13, 84, 580, 4216, 31824, 247168, 1962800, 15866016, 130122304, 1080101760, 9057113472, 76610188544, 652895283200, 5600752756224, 48323092761344, 419068973537792, 3650909105378304, 31937405800724480, 280419948474447872, 2470473454986891264
Offset: 0
Keywords
Programs
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PARI
a(n, r=2, s=3, t=3, 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)^(3/2) / (1-x)^3 )^2.
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)^2, where B(x) is the g.f. of A213282.