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%I #5 Sep 22 2017 10:44:34
%S 1,1,4,14,67,343,2151,9860,53739,279360,1595454,8733436,53035750,
%T 280946972,1626421033,9103196607,53266673126,300953629850,
%U 1817236258604,10114067087883,59666856128423,342703064143223,2024687556279346,11644875879288821,70172335165701018
%N Number of multisets of nonempty words with a total of n letters over 6-ary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H Alois P. Heinz, <a href="/A292721/b292721.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{j>=1} 1/(1-x^j)^A226876(j).
%F Euler transform of A226876.
%p b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
%p add(b(n-j, j, t-1)/j!, j=i..n/t))
%p end:
%p a:= proc(n) option remember; `if`(n=0, 1, add(add(d*d!*
%p b(d, 0, 6), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
%p end:
%p seq(a(n), n=0..35);
%Y Column k=6 of A292712.
%Y Cf. A226876, A226873.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 21 2017
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