A378460 - OEIS

%I #11 Nov 27 2024 07:11:52

%S 1,2,14,107,854,6997,58337,492459,4195910,36008585,310797519,

%T 2695146412,23462692889,204927930573,1794924637121,15759722754487,

%U 138667548834150,1222405694908165,10793913082306739,95452822514557693,845239550997448559,7493699336086875984

%N a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(2*n+k-1,n-k).

%F a(n) = [x^n] 1/(1 - x - x/(1 - x))^n.

%F 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

%o (PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(2*n+k-1, n-k));

%Y Cf. A009723, A378461.

%Y Cf. A378465.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 27 2024