%I #5 Jan 06 2021 20:18:14
%S 1,1,3,13,60,326,1345,6228,29845,143899,732765,3412167,16623175,
%T 81624325,400892932,2018593583,9773821243,48292202375,239383150209,
%U 1186254809797,5960931333905,29322695430795,145800954979162,726137079681765,3616351096084351
%N Number of sets of nonempty words with a total of n letters over quinary 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="/A340412/b340412.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{j>=1} (1+x^j)^A226875(j).
%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 g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
%p h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
%p end:
%p a:= n-> h(n$2, min(n, 5)):
%p seq(a(n), n=0..32);
%Y Column k=5 of A292795.
%Y Cf. A226875.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Jan 06 2021