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

1, 2, 16, 288, 10240, 700416, 92864512, 24184487936, 12484798840832, 12835745584644096, 26339606633209921536, 107993030830149951553536, 885112171099428768672907264, 14505223494706550858367937544192, 475365227058478388903633481696804864

Offset: 0

Author

Michael Somos, Feb 06 2015

Keywords

• nonn

Comments

In Blieberger and Kirschenhofer 2014 denoted by r_n on page 106 equation (5).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..80
• J. Blieberger and P. Kirschenhofer, Generalized Catalan Sequences Originating from the Analysis of Special Data Structures, Bulletin of the ICA, 71 (2014) 103-116.

Programs

Haskell

a254744 n = a254744_list !! n
a254744_list = 1 : f 2 [1] where
   f x ys = y : f (x * 2) (y : ys) where
            y = x * (sum $ zipWith (*) ys $ reverse ys)
-- Reinhard Zumkeller, Feb 07 2015

PARI

{a(n) = if( n<1, n==0, 2^n * sum(k=0, n-1, a(k) * a(n-1-k)))};

Formula

a(n) ~ 2^((n^2 + 3*n)/2) * c where c = 0.7153374336... .