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A254744 a(n) = 2^n * Sum_{k=1 .. n-1} a(k) * a(n-1-k) with a(0) = 1.

%I A254744 #11 Feb 07 2015 11:37:40
%S A254744 1,2,16,288,10240,700416,92864512,24184487936,12484798840832,
%T A254744 12835745584644096,26339606633209921536,107993030830149951553536,
%U A254744 885112171099428768672907264,14505223494706550858367937544192,475365227058478388903633481696804864
%N A254744 a(n) = 2^n * Sum_{k=1 .. n-1} a(k) * a(n-1-k) with a(0) = 1.
%C A254744 In Blieberger and Kirschenhofer 2014 denoted by r_n on page 106 equation (5).
%H A254744 Reinhard Zumkeller, <a href="/A254744/b254744.txt">Table of n, a(n) for n = 0..80</a>
%H A254744 J. Blieberger and P. Kirschenhofer, <a href="http://institute.unileoben.ac.at/mathstat/personal/(2014)%20Generalized%20Catalan%20Sequences%20%5BEtc%5D.pdf">Generalized Catalan Sequences Originating from the Analysis of Special Data Structures</a>, Bulletin of the ICA, 71 (2014) 103-116.
%F A254744 a(n) ~ 2^((n^2 + 3*n)/2) * c where c = 0.7153374336... .
%o A254744 (PARI) {a(n) = if( n<1, n==0, 2^n * sum(k=0, n-1, a(k) * a(n-1-k)))};
%o A254744 (Haskell)
%o A254744 a254744 n = a254744_list !! n
%o A254744 a254744_list = 1 : f 2 [1] where
%o A254744    f x ys = y : f (x * 2) (y : ys) where
%o A254744             y = x * (sum $ zipWith (*) ys $ reverse ys)
%o A254744 -- _Reinhard Zumkeller_, Feb 07 2015
%K A254744 nonn
%O A254744 0,2
%A A254744 _Michael Somos_, Feb 06 2015