A372139 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1 + 4*x)^(1/2) * A(x)^2 ).
1, 1, 5, 22, 131, 775, 5018, 33066, 225915, 1569663, 11114665, 79715150, 578603008, 4239698240, 31329174328, 233166912152, 1746351112863, 13152340002195, 99545267265903, 756752801436930, 5775810585852675, 44241685802126865, 339991810347999194
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Keywords
Programs
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PARI
a(n) = sum(k=0, n, 4^(n-k)*binomial(3*k, k)*binomial(k/2, n-k)/(2*k+1));
Formula
a(n) = Sum_{k=0..n} 4^(n-k) * binomial(3*k,k) * binomial(k/2,n-k)/(2*k+1).