%I
%S 1,5040,135135,210455470,1428739165560,23060727168393236,
%T 668821362774214965294,29745278219128813035415595,
%U 1835364055105945091130559202709,146812609193179942830629976945746464,14506158303190746913523011613729321067580
%N Number of words w where each letter of the 7ary 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 ith letter in z.
%e a(0) = 1: the empty word.
%e a(1) = 5040: abcdefg, abcdegf, abcdfeg, ..., gfedbca, gfedcab, gfedcba, (all permutations of 7 letters).
%e a(2) = 135135: aabbccddeeffgg, aabbccddeefgfg, aabbccddeegffg], ..., gfedcaabbcdefg, gfedcababcdefg, gfedcbaabcdefg.
%Y Column k=7 of A213275.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Jun 23 2012
