A379330 G.f. A(x) satisfies A(x) = 1/sqrt( (1 - 2*x*A(x)^2) * (1 - 2*x*A(x)) ).
1, 2, 10, 66, 500, 4112, 35702, 322114, 2990450, 28382486, 274151074, 2686200302, 26634199776, 266738477892, 2694291026378, 27416542767134, 280790643343716, 2892142875601024, 29939599990333394, 311334925950172590, 3250627732373638716, 34063930480000774400, 358149513590192454578
Offset: 0
Keywords
Programs
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PARI
a(n) = 2^n*sum(k=0, n, binomial(n/2+3*k/2+1/2, k)*binomial(3*n/2-k/2-1/2, n-k)/(n+3*k+1));
Formula
a(n) = 2^n * Sum_{k=0..n} binomial(n/2+3*k/2+1/2,k) * binomial(3*n/2-k/2-1/2,n-k)/(n+3*k+1).