A340412 Number of sets of nonempty words with a total of n letters over quinary 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, 1345, 6228, 29845, 143899, 732765, 3412167, 16623175, 81624325, 400892932, 2018593583, 9773821243, 48292202375, 239383150209, 1186254809797, 5960931333905, 29322695430795, 145800954979162, 726137079681765, 3616351096084351

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)^A226875(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, 5)):
seq(a(n), n=0..32);

Crossrefs

Column k=5 of A292795.

Cf. A226875.

Sequence in context: A357151 A367058 A353208 * A340413 A340414 A340415

Adjacent sequences: A340409 A340410 A340411 * A340413 A340414 A340415

Keyword

nonn

Author

Alois P. Heinz, Jan 06 2021

Status

approved