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 A370213 #12 Feb 12 2024 08:38:47
%S A370213 1,2,6,23,102,477,2265,10831,52134,252581,1230831,6027012,29630793,
%T A370213 146162525,723042585,3585576123,17819138214,88723077165,442503268107,
%U A370213 2210287317913,11055220684527,55362552116104,277553123875572,1392884816721228,6996589905913737
%N A370213 Coefficient of x^n in the expansion of ( (1+x)^2 / (1-x^3) )^n.
%F A370213 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(2*n,n-3*k).
%F A370213 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) ). See A369398.
%o A370213 (PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial(u*n, n-s*k));
%Y A370213 Cf. A369398.
%K A370213 nonn
%O A370213 0,2
%A A370213 _Seiichi Manyama_, Feb 12 2024