%I
%S 6,48,274,1338,6035,25874,108002,444458,1818905,7451418,30693022,
%T 127604480,536876960,2291507552,9939572897,43885543586,197465168488,
%U 906430558822,4247727231198,20333276583188,99450038211268,497066503157976,2538584563166367
%N Number of sets of exactly five nonempty words with a total of n letters over nary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H Alois P. Heinz, <a href="/A293967/b293967.txt">Table of n, a(n) for n = 11..807</a>
%F a(n) = [x^n y^5] Product_{j>=1} (1+y*x^j)^A000085(j).
%p g:= proc(n) option remember; `if`(n<2, 1, g(n1)+(n1)*g(n2)) end:
%p b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p add(b(ni*j, i1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 6)
%p end:
%p a:= n> coeff(b(n$2), x, 5):
%p seq(a(n), n=11..35);
%Y Column k=5 of A293815.
%Y Cf. A000085.
%K nonn
%O 11,1
%A _Alois P. Heinz_, Oct 20 2017
