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 A370620 #16 May 02 2024 09:49:25
%S A370620 1,3,27,255,2535,25908,269667,2843214,30264975,324543495,3500669172,
%T A370620 37940361660,412830243735,4507040972190,49345845670470,
%U A370620 541602648192480,5957253066586815,65650003858745514,724693081872783375,8011727857439155500,88692087094226151300
%N A370620 Coefficient of x^n in the expansion of 1 / (1-x-x^2)^(3*n).
%F A370620 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(4*n-k-1,n-2*k).
%F A370620 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x-x^2)^3 ). See A368963.
%t A370620 a[n_]:=SeriesCoefficient[(1-x-x^2)^(-3*n),{x,0,n}]; Array[a,21,0] (* _Stefano Spezia_, May 01 2024 *)
%o A370620 (PARI) a(n, s=2, t=3, u=0) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
%Y A370620 Cf. A370621, A370622, A370623.
%Y A370620 Cf. A368963.
%K A370620 nonn
%O A370620 0,2
%A A370620 _Seiichi Manyama_, May 01 2024