A292725 - OEIS

%I #5 Sep 22 2017 11:30:20

%S 1,1,4,14,67,343,2151,14900,119259,1055520,10465854,73562956,

%T 592088950,4560084092,37322365393,303133205967,2640424710926,

%U 22786686453050,210764523790244,1891228958070987,18197644702881767,155143878113188799,1411297482751989322

%N Number of multisets of nonempty words with a total of n letters over 10-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="/A292725/b292725.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{j>=1} 1/(1-x^j)^A226880(j).

%F Euler transform of A226880.

%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, 10), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)

%p     end:

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

%Y Column k=10 of A292712.

%Y Cf. A226880, A226873.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 21 2017