cp's OEIS Frontend

A292725 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.

%I A292725 #5 Sep 22 2017 11:30:20
%S A292725 1,1,4,14,67,343,2151,14900,119259,1055520,10465854,73562956,
%T A292725 592088950,4560084092,37322365393,303133205967,2640424710926,
%U A292725 22786686453050,210764523790244,1891228958070987,18197644702881767,155143878113188799,1411297482751989322
%N A292725 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 A292725 Alois P. Heinz, <a href="/A292725/b292725.txt">Table of n, a(n) for n = 0..1000</a>
%F A292725 G.f.: Product_{j>=1} 1/(1-x^j)^A226880(j).
%F A292725 Euler transform of A226880.
%p A292725 b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
%p A292725       add(b(n-j, j, t-1)/j!, j=i..n/t))
%p A292725     end:
%p A292725 a:= proc(n) option remember; `if`(n=0, 1, add(add(d*d!*
%p A292725       b(d, 0, 10), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
%p A292725     end:
%p A292725 seq(a(n), n=0..35);
%Y A292725 Column k=10 of A292712.
%Y A292725 Cf. A226880, A226873.
%K A292725 nonn
%O A292725 0,3
%A A292725 _Alois P. Heinz_, Sep 21 2017