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%I #2 Mar 30 2012 18:59:14
%S 1,4,21,109,575,3047,16192,86171,458972,2445825,13037508,69509558,
%T 370634265,1976421031,10539858413,56208784808,299766435277,
%U 1598704176149,8526238418811,45472594256564,242517996824355
%N Expansion of 1/((1-4*x*c(x))(1-x^2*c(x))), c(x) the g.f. of A000108.
%C Diagonal sums of number triangle A117380.
%F a(n)=sum{k=0..floor(n/2), [k<=n-k]*sum{j=0..n-k, (j/(n-k-j))*C(2n-k-j,n-k-j)[k<=j]*4^(j-k)}}
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 10 2006