A340415 Number of sets of nonempty words with a total of n letters over octonary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

1, 1, 3, 13, 60, 326, 2065, 14508, 116845, 676579, 4533285, 29337447, 204274255, 1401597565, 10464806200, 75242714351, 588938921227, 4060713617519, 30141138974325, 217182619165093, 1630762746458645, 11987353708674543, 91946531392941646, 683807822490949653

Offset

0,3

Links

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

Formula

G.f.: Product_{j>=1} (1+x^j)^A226878(j).

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:
g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
    end:
a:= n-> h(n$2, min(n, 8)):
seq(a(n), n=0..32);

Crossrefs

Column k=8 of A292795.

Cf. A226878.

Sequence in context: A340412 A340413 A340414 * A340416 A340417 A292796

Adjacent sequences: A340412 A340413 A340414 * A340416 A340417 A340418

Keyword

nonn

Author

Alois P. Heinz, Jan 06 2021

Status

approved