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%I #6 Mar 30 2012 18:55:30
%S 1,5,51,618,8043,108753,1505652,21181632,301445115,4327546335,
%T 62550664827,909065484726,13271032349844,194464001709708,
%U 2858582670411768,42135099729748512,622533141544186779,9216768941364987195,136706015987753749593
%N Central coefficients of the Riordan matrix A121576.
%F a(n) = [x^n](1-2*x-2*x^2)*(1+2*x)^(2*n)/(1-x)^(2*n+1).
%F a(n) = sum(i=0..n, binomial(2*n,i) * binomial(3*n-i,2*n) * (8*n^2-12*(i-1)*n+3*i^2-9*i+4) / ((2*n-i+2)*(2*n-i+1))*2^i)/2
%t Sum[Binomial[2n,i]Binomial[3n-i,2n](4-9i+3i^2-12(i-1)n+8n^2)/((2n-i+2)(2n-i+1))2^i,{i,0,n}]/2
%o (Maxima) makelist(sum(binomial(2*n,i)*binomial(3*n-i,2*n)*(4-9*i+3*i^2-12*(i-1)*n+8*n^2)/((2*n-i+2)*(2*n-i+1))*2^i,i,0,n)/2,n,0,12);
%Y Cf. A121576.
%K nonn
%O 0,2
%A _Emanuele Munarini_, May 18 2011
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