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.

1, 1, 4, 14, 67, 343, 2151, 14900, 119259, 1055520, 10465854, 73562956, 592088950, 4560084092, 37322365393, 303133205967, 2640424710926, 22786686453050, 210764523790244, 1891228958070987, 18197644702881767, 155143878113188799, 1411297482751989322

Offset: 0

Author

Alois P. Heinz, Sep 21 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=10 of A292712.

Cf. A226880, A226873.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
      add(b(n-j, j, t-1)/j!, j=i..n/t))
    end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*d!*
      b(d, 0, 10), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..35);

Formula

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

Euler transform of A226880.