This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378460 #11 Nov 27 2024 07:11:52
%S A378460 1,2,14,107,854,6997,58337,492459,4195910,36008585,310797519,
%T A378460 2695146412,23462692889,204927930573,1794924637121,15759722754487,
%U A378460 138667548834150,1222405694908165,10793913082306739,95452822514557693,845239550997448559,7493699336086875984
%N A378460 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(2*n+k-1,n-k).
%F A378460 a(n) = [x^n] 1/(1 - x - x/(1 - x))^n.
%F A378460 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 A378460 (PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(2*n+k-1, n-k));
%Y A378460 Cf. A009723, A378461.
%Y A378460 Cf. A378465.
%K A378460 nonn
%O A378460 0,2
%A A378460 _Seiichi Manyama_, Nov 27 2024