A378460 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(2*n+k-1,n-k).
1, 2, 14, 107, 854, 6997, 58337, 492459, 4195910, 36008585, 310797519, 2695146412, 23462692889, 204927930573, 1794924637121, 15759722754487, 138667548834150, 1222405694908165, 10793913082306739, 95452822514557693, 845239550997448559, 7493699336086875984
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(2*n+k-1, n-k));
Formula
a(n) = [x^n] 1/(1 - x - x/(1 - x))^n.
a(n) ~ ((16 + 12*2^(1/3) + 9*2^(2/3))/5)^n * sqrt((1 + 2^(2/3))/(12*Pi*n)). - Vaclav Kotesovec, Nov 27 2024