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%I #9 Aug 31 2013 19:33:49
%S 1,1,2,4,9,20,48,115,286,719,1842,4766,12485,32969,87795,235326,
%T 634664,1720573,4686829,12820504,35204254,97001655,268120807,
%U 743236814,2065709551,5755253457
%N Number of distinct values taken by 9^9^...^9 (with n 9's and parentheses inserted in all possible ways).
%C The subsequence of primes begins 2, 719, 32969. No more through a(26). [Jonathan Vos Post, Apr 02 2011]
%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 Jonathan Vos Post, <a href="http://magicdragon.com/EmeraldCity/Nonfiction/four9s.html">The Four Nines problem</a>.
%H <a href="/index/Par#parens">Index entries for sequences related to parenthesizing</a>
%Y Cf. A002845, A003018, A003019, A145545, A145546, A145547, A145548, A145550, A000081.
%K more,nonn
%O 1,3
%A _Jon E. Schoenfield_, Oct 13 2008
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