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 A370622 #15 May 02 2024 09:49:18
%S A370622 1,1,9,46,293,1806,11538,74173,482157,3154645,20762014,137270376,
%T A370622 911111522,6067104434,40514133081,271195540971,1819188150365,
%U A370622 12225956834430,82301499780885,554850642658483,3745615502285478,25315915432984852,171292993893095996
%N A370622 Coefficient of x^n in the expansion of ( (1-x)^2 / (1-x-x^2)^3 )^n.
%F A370622 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(2*n-k-1,n-2*k).
%F A370622 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)^2 ). See A369488.
%t A370622 a[n_]:=SeriesCoefficient[((1-x)^2/(1-x-x^2)^3)^n,{x,0,n}]; Array[a,23,0] (* _Stefano Spezia_, May 01 2024 *)
%o A370622 (PARI) a(n, s=2, t=3, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
%Y A370622 Cf. A370620, A370621, A370623.
%Y A370622 Cf. A369488.
%K A370622 nonn
%O A370622 0,3
%A A370622 _Seiichi Manyama_, May 01 2024