A292720 - OEIS

%I #5 Sep 22 2017 10:40:04

%S 1,1,4,14,67,343,1431,6620,31539,151680,769374,3586756,17500630,

%T 85727012,420986605,2116435479,10254063794,50697425138,251055167912,

%U 1244053731675,6246442090103,30737278735067,152890117563022,761050222982081,3790169351183134

%N Number of multisets of nonempty words with a total of n letters over 5-ary 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="/A292720/b292720.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{j>=1} 1/(1-x^j)^A226875(j).

%F Euler transform of A226875.

%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 a:= proc(n) option remember; `if`(n=0, 1, add(add(d*d!*

%p       b(d, 0, 5), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)

%p     end:

%p seq(a(n), n=0..35);

%Y Column k=5 of A292712.

%Y Cf. A226875, A226873.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 21 2017