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 A378566 #9 Dec 01 2024 06:14:58
%S A378566 1,1,9,64,465,3456,26082,199060,1532313,11875015,92528414,724187982,
%T A378566 5689127886,44834549501,354289977750,2806262293824,22273793685609,
%U A378566 177113634045858,1410633764438967,11251419724586850,89860413370562730,718528004169570925
%N A378566 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+2*k-1,n-k).
%F A378566 a(n) = [x^n] 1/(1 - x/(1 - x)^3)^n.
%o A378566 (PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(n+2*k-1, n-k));
%Y A378566 Cf. A002002, A378565, A378567.
%Y A378566 Cf. A052529, A362088, A365150.
%K A378566 nonn
%O A378566 0,3
%A A378566 _Seiichi Manyama_, Dec 01 2024