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%I #10 May 01 2024 08:59:23
%S 1,0,2,3,14,35,125,371,1238,3909,12847,41580,136577,447187,1473341,
%T 4855703,16053830,53138243,176233967,585202261,1945964079,6478043120,
%U 21588979876,72016891508,240452892569,803489258285,2686964354375,8991840800136,30110638705889
%N Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2) )^n.
%F a(n) = Sum_{k=0..floor(n/2)} binomial(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) / (1-x) ).
%o (PARI) a(n, s=2, t=1, u=1) = 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. A046736, A213684.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 30 2024