cp's OEIS Frontend

A340412 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.

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