A340415 - OEIS

%I #5 Jan 06 2021 20:56:57

%S 1,1,3,13,60,326,2065,14508,116845,676579,4533285,29337447,204274255,

%T 1401597565,10464806200,75242714351,588938921227,4060713617519,

%U 30141138974325,217182619165093,1630762746458645,11987353708674543,91946531392941646,683807822490949653

%N 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 Alois P. Heinz, <a href="/A340415/b340415.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{j>=1} (1+x^j)^A226878(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, 8)):

%p seq(a(n), n=0..32);

%Y Column k=8 of A292795.

%Y Cf. A226878.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jan 06 2021