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Number of distinct values taken by 6^6^...^6 (with n 6's and parentheses inserted in all possible ways).
15

%I #8 Oct 05 2017 02:53:32

%S 1,1,2,4,9,20,48,115,286,718,1838,4750,12431,32790,87225,233534,

%T 629123,1703586,4635181,12664335,34734322,95592704,263909594

%N Number of distinct values taken by 6^6^...^6 (with n 6'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 <a href="/index/Par#parens">Index entries for sequences related to parenthesizing</a>

%Y Cf. A002845, A003018, A003019, A145545, A145547, A145548, A145549, A145550, A000081.

%K more,nonn

%O 1,3

%A _Jon E. Schoenfield_, Oct 13 2008