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 A378567 #11 Dec 01 2024 10:54:42
%S A378567 1,1,11,88,715,5951,50288,429696,3702987,32125390,280211701,
%T A378567 2454992618,21588647392,190444368401,1684556756320,14935618142768,
%U A378567 132695019071499,1181070210132582,10529299131757754,94005323670592130,840373149466892965,7521508912742542806
%N A378567 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+3*k-1,n-k).
%F A378567 a(n) = [x^n] 1/(1 - x/(1 - x)^4)^n.
%t A378567 a[n_]:=SeriesCoefficient[ 1/(1 - x/(1 - x)^4)^n,{x,0,n}]; Array[a,22,0] (* _Stefano Spezia_, Dec 01 2024 *)
%o A378567 (PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(n+3*k-1, n-k));
%Y A378567 Cf. A002002, A378565, A378566.
%Y A378567 Cf. A055991, A367234.
%K A378567 nonn
%O A378567 0,3
%A A378567 _Seiichi Manyama_, Dec 01 2024