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Bisection of A007059.
2

%I #14 Dec 22 2016 17:29:22

%S 1,2,5,14,43,140,472,1628,5719,20388,73562,268066,984911,3643570,

%T 13557020,50691978,190353370,717457656,2713061899,10289600164,

%U 39127877886,149147692734,569767908076,2180978471298,8363866011929,32129445138352,123618810558184

%N Bisection of A007059.

%D R. Kemp, Balanced ordered trees, Random Structures and Algorithms, 5, 1994, 99-121.

%H Alois P. Heinz, <a href="/A066351/b066351.txt">Table of n, a(n) for n = 0..500</a>

%F Conjecture: a(n) ~ 0.721... * 4^n / n. - _Vaclav Kotesovec_, Aug 25 2014

%p b:= proc(n, m) option remember; `if`(n=0, 1,

%p `if`(m=0, add(b(n-j, j), j=1..n),

%p add(b(n-j, min(n-j, m)), j=1..min(n, m))))

%p end:

%p a:= n-> b(2*n, 0):

%p seq(a(n), n=0..40); # _Alois P. Heinz_, May 13 2014

%t b[n_, m_] := b[n, m] = If[n == 0, 1, If[m == 0, Sum[b[n - j, j], {j, 1, n} ], Sum[b[n - j, Min[n - j, m]], {j, 1, Min[n, m]}]]]; a[n_] := b[2*n, 0]; Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Dec 22 2016, after _Alois P. Heinz_ *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 19 2001

%E More terms from _Emeric Deutsch_, Jun 10 2004