cp's OEIS Frontend

A292723 Number of multisets of nonempty words with a total of n letters over 8-ary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%I A292723 #5 Sep 22 2017 10:54:41
%S A292723 1,1,4,14,67,343,2151,14900,119259,692640,4659774,30077836,209311030,
%T A292723 1433872892,10689029713,76772260527,600293120366,4142024767610,
%U A292723 30775147154084,221566161988587,1663421685691847,12221938274124959,93706886872251562,696726353909296853
%N A292723 Number of multisets of nonempty words with a total of n letters over 8-ary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H A292723 Alois P. Heinz, <a href="/A292723/b292723.txt">Table of n, a(n) for n = 0..1000</a>
%F A292723 G.f.: Product_{j>=1} 1/(1-x^j)^A226878(j).
%F A292723 Euler transform of A226878.
%p A292723 b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
%p A292723       add(b(n-j, j, t-1)/j!, j=i..n/t))
%p A292723     end:
%p A292723 a:= proc(n) option remember; `if`(n=0, 1, add(add(d*d!*
%p A292723       b(d, 0, 8), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
%p A292723     end:
%p A292723 seq(a(n), n=0..35);
%Y A292723 Column k=8 of A292712.
%Y A292723 Cf. A226878, A226873.
%K A292723 nonn
%O A292723 0,3
%A A292723 _Alois P. Heinz_, Sep 21 2017