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 A378611 #12 Dec 02 2024 10:09:37
%S A378611 1,2,14,104,806,6412,51908,425476,3520070,29332940,245841284,
%T A378611 2070093632,17499188924,148414157816,1262280506144,10762045739644,
%U A378611 91951462167110,787113739061260,6749009521216052,57954807274992208,498334047795436276,4290199618047230824
%N A378611 a(n) = Sum_{k=0..n} binomial(2*n+k-1,k) * binomial(n-1,n-k).
%F A378611 a(n) = [x^n] 1/(1 - x/(1 - x))^(2*n).
%F A378611 a(n) = (1/2)^n * [x^(2*n)] 2/(1 - x/(1 - x))^n for n > 0.
%F A378611 a(n) = 2 * A259554(n) for n > 0.
%o A378611 (PARI) a(n) = sum(k=0, n, binomial(2*n+k-1, k)*binomial(n-1, n-k));
%Y A378611 Cf. A002002, A378612, A378613.
%Y A378611 Cf. A211789, A259554.
%K A378611 nonn
%O A378611 0,2
%A A378611 _Seiichi Manyama_, Dec 01 2024