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 A370623 #16 May 02 2024 09:49:14
%S A370623 1,0,6,9,90,255,1671,6258,34674,148455,765141,3499551,17487531,
%T A370623 82704921,408192420,1964826174,9657348546,46944246777,230604062127,
%U A370623 1127574041325,5543828629305,27211172907207,133970970691311,659351846223252,3251029812112995
%N A370623 Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2) )^(3*n).
%F A370623 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(n-k-1,n-2*k).
%F A370623 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 / (1-x)^3 ). See A369013.
%t A370623 a[n_]:=SeriesCoefficient[((1-x)/(1-x-x^2))^(3n),{x,0,n}]; Array[a,25,0] (* _Stefano Spezia_, May 01 2024 *)
%o A370623 (PARI) a(n, s=2, t=3, u=3) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
%Y A370623 Cf. A370620, A370621, A370622.
%Y A370623 Cf. A369013.
%K A370623 nonn
%O A370623 0,3
%A A370623 _Seiichi Manyama_, May 01 2024