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A254744
a(n) = 2^n * Sum_{k=1 .. n-1} a(k) * a(n-1-k) with a(0) = 1.
2
1, 2, 16, 288, 10240, 700416, 92864512, 24184487936, 12484798840832, 12835745584644096, 26339606633209921536, 107993030830149951553536, 885112171099428768672907264, 14505223494706550858367937544192, 475365227058478388903633481696804864
OFFSET
0,2
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.
FORMULA
a(n) ~ 2^((n^2 + 3*n)/2) * c where c = 0.7153374336... .
PROG
(PARI) {a(n) = if( n<1, n==0, 2^n * sum(k=0, n-1, a(k) * a(n-1-k)))};
(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
CROSSREFS
Sequence in context: A136796 A055546 A009549 * A009795 A182562 A112722
KEYWORD
nonn
AUTHOR
Michael Somos, Feb 06 2015
STATUS
approved