A340414 Number of sets of nonempty words with a total of n letters over septenary 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, 76525, 454819, 2718885, 16777767, 107808655, 697287805, 4748992600, 29397584111, 190989109387, 1239766891439, 8159345112885, 54161955000133, 360150593097845, 2454684519628143, 16056425089104526, 107300319826659573

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)^A226877(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, 7)):
seq(a(n), n=0..32);

Crossrefs

Column k=7 of A292795.

Cf. A226877.

Sequence in context: A353208 A340412 A340413 * A340415 A340416 A340417

Adjacent sequences: A340411 A340412 A340413 * A340415 A340416 A340417

Keyword

nonn

Author

Alois P. Heinz, Jan 06 2021

Status

approved