A371613 G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3) )^2.
1, 2, 3, 16, 83, 460, 2767, 17210, 110308, 723624, 4832363, 32747106, 224619408, 1556484636, 10879744696, 76621739626, 543159825499, 3872610857558, 27752175177823, 199787917082084, 1444171829169939, 10477887409768628, 76275565075016394
Offset: 0
Keywords
Programs
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PARI
a(n, r=2, s=1, t=0, u=6) = 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
a(n) = Sum_{k=0..n} binomial(6*(n-k)+2,k) * binomial(n-1,n-k)/(3*(n-k)+1).