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%I #3 Mar 30 2012 18:58:59
%S 1,1,3,6,21,54,186,479,1938,5795,22888,70781,286443,861463,3592105,
%T 11492256,39274353,148852401,613876868,1917516257,8511689170,
%U 25445125513,100975365920,390096404027,1666653892303,5319341488465
%N Diagonal sums of a matrix associated to the inverse of a Catalan scaled binomial matrix.
%C Diagonal sums of A098509.
%F a(n)=sum{k=0..floor(n/2), denominator((n-k+1)Binomial(n-k, k)/Binomial(2(n-k), n-k))}
%K easy,nonn
%O 0,3
%A _Paul Barry_, Sep 11 2004