%I #4 Jun 24 2012 12:58:43

%S 1,720,10395,3864040,4622269345,10915151070941,40684710729862072,

%T 211109968702038259993,1409438188685787895321841,

%U 11481253272835564584899247346,109898940874611419792791074271620,1202306852636261419990922606451803760

%N Number of words w where each letter of the 6-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) = 720: abcdef, abcdfe, abcedf, ..., fedbca, fedcab, fedcba.

%e a(2) = 10395: aabbccddeeff, aabbccddefef, aabbccddfeef, ..., fedcaabbcdef, fedcababcdef, fedcbaabcdef.

%Y Column k=6 of A213275.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jun 23 2012