cp's OEIS Frontend

A340415 Number of sets of nonempty words with a total of n letters over octonary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%I A340415 #5 Jan 06 2021 20:56:57
%S A340415 1,1,3,13,60,326,2065,14508,116845,676579,4533285,29337447,204274255,
%T A340415 1401597565,10464806200,75242714351,588938921227,4060713617519,
%U A340415 30141138974325,217182619165093,1630762746458645,11987353708674543,91946531392941646,683807822490949653
%N A340415 Number of sets of nonempty words with a total of n letters over octonary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H A340415 Alois P. Heinz, <a href="/A340415/b340415.txt">Table of n, a(n) for n = 0..1000</a>
%F A340415 G.f.: Product_{j>=1} (1+x^j)^A226878(j).
%p A340415 b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
%p A340415       add(b(n-j, j, t-1)/j!, j=i..n/t))
%p A340415     end:
%p A340415 g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
%p A340415 h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A340415       add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
%p A340415     end:
%p A340415 a:= n-> h(n$2, min(n, 8)):
%p A340415 seq(a(n), n=0..32);
%Y A340415 Column k=8 of A292795.
%Y A340415 Cf. A226878.
%K A340415 nonn
%O A340415 0,3
%A A340415 _Alois P. Heinz_, Jan 06 2021