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%I #10 May 30 2019 09:27:58
%S 1,1,3,7,20,54,164,499,1621,5397,18762,67000,247439,936167,3639968,
%T 14450634,58677742,242511781,1021307520,4365923278,18960435664,
%U 83395216882,371734296357,1675125941350,7635063496721,35127842511275,163213032700613,764541230737345
%N Number of multisets of nonempty words with a total of n letters over senary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%C This sequence differs from A293110 first at n=7.
%H Alois P. Heinz, <a href="/A293736/b293736.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{j>=1} 1/(1-x^j)^A007579(j).
%F a(n) ~ c * 6^n / n^(15/2), where c = 121210.8807171702661881473876689430182129891246619701141888082152779... - _Vaclav Kotesovec_, May 30 2019
%p g:= proc(n) option remember;
%p `if`(n<4, [1, 1, 2, 4][n+1], ((20*n^2+184*n+336)*g(n-1)
%p +4*(n-1)*(10*n^2+58*n+33)*g(n-2) -144*(n-1)*(n-2)*g(n-3)
%p -144*(n-1)*(n-2)*(n-3)*g(n-4))/ ((n+5)*(n+8)*(n+9)))
%p end:
%p a:= proc(n) option remember; `if`(n=0, 1, add(add(g(d)
%p *d, 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 A293108.
%Y Cf. A007579, A293110, A293745.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Oct 15 2017
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