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

Author

Alois P. Heinz, Jan 06 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=7 of A292795.

Cf. A226877.

Programs

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);

Formula

G.f.: Product_{j>=1} (1+x^j)^A226877(j).