A379383 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x))/(1 - 2*x*A(x)^3) ).
1, 2, 10, 80, 750, 7680, 83252, 939008, 10905942, 129548288, 1566565452, 19220267008, 238662840780, 2993651974144, 37876206019560, 482802294325248, 6194365014836582, 79930063134392320, 1036640587694252380, 13505632613590630400, 176673045664669396132, 2319654465118014537728
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Keywords
Programs
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PARI
a(n) = 2^n*sum(k=0, n, binomial(n/2+2*k-1/2, k)*binomial(n/2+k+1/2, n-k)/(n+2*k+1));
Formula
a(n) = 2^n * Sum_{k=0..n} binomial(n/2+2*k-1/2,k) * binomial(n/2+k+1/2,n-k)/(n+2*k+1).
a(n) = 2^n * Sum_{k=0..n} binomial(n,k) * binomial(n/2+2*k+1/2,n)/(n+4*k+1).