login
Number of distinct values taken by 5^5^...^5 (with n 5's and parentheses inserted in all possible ways).
15

%I #11 Oct 05 2017 02:53:25

%S 1,1,2,4,9,20,48,115,285,715,1826,4711,12303,32387,85964,229662,

%T 617300,1667787,4527290,12340688,33766612,92707834,255329106

%N Number of distinct values taken by 5^5^...^5 (with n 5's and parentheses inserted in all possible ways).

%H R. K. Guy and J. L. Selfridge, <a href="http://www.jstor.org/stable/2319392">The nesting and roosting habits of the laddered parenthesis</a>, Amer. Math. Monthly 80 (8) (1973), 868-876.

%H MathOverflow, <a href="http://mathoverflow.net/questions/79442/number-of-distinct-values-taken-by-xx-x-with-parentheses-inserted-in-all-pos">MathOverflow discussion of related questions</a>

%H <a href="/index/Par#parens">Index entries for sequences related to parenthesizing</a>

%Y Cf. A002845, A003018, A003019, A145546, A145547, A145548, A145549, A145550, A000081.

%K more,nonn

%O 1,3

%A _Jon E. Schoenfield_, Oct 13 2008