A340413 Number of sets of nonempty words with a total of n letters over senary 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, 9468, 51325, 268339, 1534485, 8421447, 51259855, 271291165, 1568129440, 8793678911, 51467662027, 290934776639, 1758652551885, 9783478684069, 57676281958781, 331610976485751, 1959129522047734, 11269354282135629, 67953764278371963

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)^A226876(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, 6)):
seq(a(n), n=0..32);

Crossrefs

Column k=6 of A292795.

Cf. A226876.

Sequence in context: A367058 A353208 A340412 * A340414 A340415 A340416

Adjacent sequences: A340410 A340411 A340412 * A340414 A340415 A340416

Keyword

nonn

Author

Alois P. Heinz, Jan 06 2021

Status

approved