A292724 Number of multisets of nonempty words with a total of n letters over 9-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, 6837054, 49975756, 358031350, 2673108092, 20399335633, 161247005007, 1321885836686, 10814140769210, 93349395210404, 726371063425227, 5939975798740967, 48195816632614079, 396235068140514442

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)^A226879(j).

Euler transform of A226879.

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

Crossrefs

Column k=9 of A292712.

Cf. A226879, A226873.

Sequence in context: A292721 A292722 A292723 * A292725 A292713 A007025

Adjacent sequences: A292721 A292722 A292723 * A292725 A292726 A292727

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2017

Status

approved