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A transform of the Catalan numbers with a simple Hankel transform.
2

%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