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 A370619 #11 May 01 2024 08:59:41
%S A370619 1,0,4,6,44,120,610,2114,9468,36384,155644,626450,2638994,10856924,
%T A370619 45565118,189579786,796023260,3333362040,14022032560,58960463548,
%U A370619 248542728364,1048148750060,4427187324102,18712146312998,79177190666034,335259593600120,1420797366753600
%N A370619 Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2) )^(2*n).
%F A370619 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(n-k-1,n-2*k).
%F A370619 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 / (1-x)^2 ). See A368957.
%o A370619 (PARI) a(n, s=2, t=2, 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 A370619 Cf. A370617, A370618.
%Y A370619 Cf. A368957.
%K A370619 nonn
%O A370619 0,3
%A A370619 _Seiichi Manyama_, May 01 2024