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%I #20 Mar 10 2023 09:27:54
%S 0,3,12,9,27,18,15,9,48,33,24,24,18,21,15,9,9,75,54,39,39,33,30,24,30,
%T 24,18,18,27,21,15,15,15,9,9,9,9,108,81,60,45,60,54,45,39,36,30,24,45,
%U 39,33,33,36,30,24,24,36,30,24,24,24,18,18,18,18,33,27
%N Third derivative of f_n at x=1, where f_n is the n-th of all functions that are representable as x^x^...^x with m>=1 x's and parentheses inserted in all possible ways.
%C For the ordering of functions f_n see A215703.
%H Alois P. Heinz, <a href="/A215842/b215842.txt">Table of n, a(n) for n = 1..7813</a>
%H D. Birmajer, J. B. Gil, M. D. Weiner, <a href="https://arxiv.org/abs/1503.05242">Colored partitions of a convex polygon by noncrossing diagonals</a>, arXiv preprint arXiv:1503.05242 [math.CO], 2015.
%p # load programs from A215703, then:
%p seq(A(3, n), n=1..100);
%Y Row n=3 of A215703.
%Y Number of distinct values of a(n) taken for functions with m x's: A199085.
%Y Cf. A000081, A087803.
%K nonn,look
%O 1,2
%A _Alois P. Heinz_, Aug 24 2012
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