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 A370217 #9 Feb 12 2024 08:39:02
%S A370217 1,2,6,29,166,927,5055,27687,153702,861950,4862481,27543111,156571951,
%T A370217 892919445,5106591405,29275176204,168181755750,967967551701,
%U A370217 5580293663274,32217589171489,186253647533841,1078046039503182,6246592211179337,36231065957573793
%N A370217 Coefficient of x^n in the expansion of ( (1+x)^2 / (1-x^3)^3 )^n.
%F A370217 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n+k-1,k) * binomial(2*n,n-3*k).
%F A370217 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3)^3 ). See A369402.
%o A370217 (PARI) a(n, s=3, t=3, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial(u*n, n-s*k));
%Y A370217 Cf. A369402.
%K A370217 nonn
%O A370217 0,2
%A A370217 _Seiichi Manyama_, Feb 12 2024