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 A370617 #10 May 01 2024 08:59:27
%S A370617 1,2,14,98,726,5522,42770,335512,2656998,21195944,170076214,
%T A370617 1371181110,11098310730,90128497032,734008622872,5992486341248,
%U A370617 49028047353670,401885885751630,3299812135410080,27134786911366212,223433635272820126,1842041118321640390
%N A370617 Coefficient of x^n in the expansion of 1 / (1-x-x^2)^(2*n).
%F A370617 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(3*n-k-1,n-2*k).
%F A370617 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)^2 ). See A368961.
%o A370617 (PARI) a(n, s=2, t=2, 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 A370617 Cf. A370618, A370619.
%Y A370617 Cf. A368961.
%K A370617 nonn
%O A370617 0,2
%A A370617 _Seiichi Manyama_, Apr 30 2024