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 A378613 #7 Dec 02 2024 10:09:46
%S A378613 1,4,44,532,6748,88024,1169444,15738328,213842716,2927097712,
%T A378613 40302226944,557565134196,7744326799684,107925260553088,
%U A378613 1508352084699224,21132667178858512,296716493251706652,4174006026061733232,58816013334014598032,830025065117154066064,11729345524163083673648
%N A378613 a(n) = Sum_{k=0..n} binomial(4*n+k-1,k) * binomial(n-1,n-k).
%F A378613 a(n) = [x^n] 1/(1 - x/(1 - x))^(4*n).
%F A378613 a(n) = (1/8)^n * [x^(4*n)] 4/(1 - x/(1 - x))^n for n > 0.
%o A378613 (PARI) a(n) = sum(k=0, n, binomial(4*n+k-1, k)*binomial(n-1, n-k));
%Y A378613 Cf. A002002, A378611, A378612.
%Y A378613 Cf. A378610.
%K A378613 nonn
%O A378613 0,2
%A A378613 _Seiichi Manyama_, Dec 01 2024