A340417 Number of sets of nonempty words with a total of n letters over denary 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, 116845, 1039459, 10339365, 72459687, 581246095, 4483235005, 36697945720, 298344453071, 2601248199787, 22469318990159, 208007606797845, 1867498245975013, 17978675539264085, 153181998023380623, 1392447676785436846

Offset: 0

Author

Alois P. Heinz, Jan 07 2021

Keywords

• nonn

Links

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

Crossrefs

Column k=10 of A292795.

Cf. A226880.

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, 10)):
seq(a(n), n=0..32);

Formula

G.f.: Product_{j>=1} (1+x^j)^A226880(j).