%I #2 Mar 30 2012 18:59:25
%S 1,0,-1,-1,1,2,1,-3,-5,-1,11,15,-5,-44,-41,51,169,85,-303,-611,-15,
%T 1513,2021,-1271,-6827,-5673,10361,28301,10141,-61102,-107015,20109,
%U 310387,356515,-354349,-1421913,-936805,2567875,5930631,972819,-14696329
%N A transform of the Catalan numbers with a simple Hankel transform.
%C Hankel transform is A157128. Partial sums of A157125.
%F G.f.: (sqrt(1+x^2+4x^3)-sqrt(1+x^2))/(2*sqrt(1+x^2));
%F a(n)=sum{k=0..n, A157125(k)};
%K easy,sign
%O 0,6
%A _Paul Barry_, Feb 23 2009