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%I #22 Mar 17 2017 23:26:56
%S 1,1,20,374,8124,190893,4727788,121543500,3212914524,86782926068,
%T 2384725558736,66456350375566,1873703883228900,53351152389518550,
%U 1531960347453263112,44311785923563130392,1289909841595078198172,37760636720455988917420,1110927659386926734186992
%N Number of words on {1,1,1,2,2,2,3,3,3,4,4,4,...,n,n,n} avoiding the pattern 123.
%H Ferenc Balogh, <a href="http://arxiv.org/abs/1505.01389">A generalization of Gessel's generating function to enumerate words with double or triple occurrences in each letter and without increasing subsequences of a given length</a>, preprint arXiv:1505.01389 [math.CO], 2015.
%H Shalosh B. Ekhad and Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/sloane75.html">The Generating Functions Enumerating 12..d-Avoiding Words with r occurrences of each of 1,2, ..., n are D-finite for all d and all r</a>, 2014
%H Nathaniel Shar, <a href="https://pdfs.semanticscholar.org/98e3/71b675789ed6ec4f9c9cd82e2dee9ca79399.pdf">Experimental methods in permutation patterns and bijective proof</a>, PhD Dissertation, Mathematics Department, Rutgers University, May 2016.
%F Conjecture: a(n) = (2/Pi)*Integral_{t=0..1} sqrt((1 - t)/t)*(64*t^3 - 32*t^2)^n = Catalan(3*n)*2F1(-1-3*n,-n;1/2-3*n;1/2). - _Benedict W. J. Irwin_, Oct 05 2016
%Y Cf. A220097, A266734, A266735, A266737-A266741.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jan 06 2016
%E More terms from _Alois P. Heinz_, Jan 14 2016
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