A340416 Number of sets of nonempty words with a total of n letters over nonary 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, 1039459, 6710565, 48872487, 350817295, 2619846205, 20019859960, 158415989711, 1300359929707, 10644485545679, 91963547963925, 715052566412773, 5842504427274965, 47435773495721103, 390005026265914606, 3225674439739003413

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)^A226879(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, 9)):
seq(a(n), n=0..32);

Crossrefs

Column k=9 of A292795.

Cf. A226879.

Sequence in context: A340413 A340414 A340415 * A340417 A292796 A020007

Adjacent sequences: A340413 A340414 A340415 * A340417 A340418 A340419

Keyword

nonn

Author

Alois P. Heinz, Jan 07 2021

Status

approved