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A generalized q-Catalan number for q=2.
1

%I #8 Dec 30 2012 11:20:04

%S 1,2,6,26,150,1114,10614,131002,2128278,46294426,1368718518,

%T 55647242106,3137452915158,246751601425242,27181289502625014,

%U 4205716133932054842,915890632125187606038,281117681559174501597466,121733516122198763782243638

%N A generalized q-Catalan number for q=2.

%C Hankel transform is A185995.

%F G.f.: 1/(1-2x/(1-x/(1-4x/(1-2x/(1-8x/(1-4x/(1-16x/(1-8x/(1-... (continued fraction).

%F G.f.: 1/(1-2x-2x^2/(1-5x-8x^2/(1-10x-32x^2/(1-(2^2+2^4)x-2^7x^2/(1-(2^3+2^5)x-2^9x^2/(1-.... (continued fraction).

%F a(n)=if(n=0,1,2*a(n-1)+sum{k=0..n-2, 2^k*a(k)*a(n-1-k)}).

%K nonn,easy

%O 0,2

%A _Paul Barry_, Feb 08 2011