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%I #7 Oct 31 2018 22:31:41
%S 1,1,3,106,115955,7236515981,40684710729862072,
%T 29745278219128813035415595,3847028733161627562733350467148495403,
%U 114752550881830601773639529476205016572641397025904,996942995951678818059423286104073541295789338859855813183302036541
%N Number of words w where each letter of the n-ary alphabet occurs n times and for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z.
%e a(0) = 1: the empty word.
%e a(1) = 1: a.
%e a(2) = 3: aabb, abab, baab.
%e a(3) = 106: aaabbbccc, aaabbcbcc, aaabbccbc, ..., cbaababcc, cbaabacbc, cbaabcabc.
%Y Main diagonal of A213275.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Jun 23 2012