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