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 A370249 #9 Feb 13 2024 08:13:34
%S A370249 1,2,10,62,394,2552,16810,112114,754698,5116832,34891260,239036470,
%T A370249 1644001546,11344059092,78497737370,544507428962,3785080540682,
%U A370249 26360971309824,183895618774084,1284778549054704,8988079638054044,62955181189933276,441442177486335002
%N A370249 Coefficient of x^n in the expansion of ( 1/(1-x)^2 * (1+x^3)^2 )^n.
%F A370249 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(3*n-3*k-1,n-3*k).
%F A370249 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)^2 ). See A369267.
%o A370249 (PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((u+1)*n-s*k-1, n-s*k));
%Y A370249 Cf. A369267, A370215.
%K A370249 nonn
%O A370249 0,2
%A A370249 _Seiichi Manyama_, Feb 13 2024