A292720 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.

1, 1, 4, 14, 67, 343, 1431, 6620, 31539, 151680, 769374, 3586756, 17500630, 85727012, 420986605, 2116435479, 10254063794, 50697425138, 251055167912, 1244053731675, 6246442090103, 30737278735067, 152890117563022, 761050222982081, 3790169351183134

Offset

0,3

Links

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

Formula

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

Euler transform of A226875.

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, 5), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..35);

Crossrefs

Column k=5 of A292712.

Cf. A226875, A226873.

Sequence in context: A347432 A129219 A292719 * A292721 A292722 A292723

Adjacent sequences: A292717 A292718 A292719 * A292721 A292722 A292723

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2017

Status

approved