A340411 Number of sets of nonempty words with a total of n letters over quaternary 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, 206, 865, 3408, 15025, 57175, 240741, 961035, 4132903, 16279273, 68134510, 274714351, 1164578487, 4657730815, 19404869767, 78676610521, 330495175277, 1332463920931, 5531856232294, 22498784991153, 93925698566719, 380437352382876

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)^A092429(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, 4)):
seq(a(n), n=0..32);

Crossrefs

Column k=4 of A292795.

Cf. A092429.

Sequence in context: A317776 A145942 A331517 * A074437 A026578 A362596

Adjacent sequences: A340408 A340409 A340410 * A340412 A340413 A340414

Keyword

nonn

Author

Alois P. Heinz, Jan 06 2021

Status

approved