A293969 Number of sets of exactly seven nonempty words with a total of n letters over n-ary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

1, 40, 394, 2766, 16251, 86162, 426894, 2021990, 9290152, 41829426, 185965908, 820999576, 3615595261, 15941247432, 70583512572, 314664832674, 1415621796873, 6439720543682, 29674662921377, 138736843637738, 659019083032289, 3184439719295586, 15669157686000028

Offset: 17

Author

Alois P. Heinz, Oct 20 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 17..813

Crossrefs

Column k=7 of A293815.

Cf. A000085.

Programs

Maple

g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 8)
    end:
a:= n-> coeff(b(n$2), x, 7):
seq(a(n), n=17..42);

Formula

a(n) = [x^n y^7] Product_{j>=1} (1+y*x^j)^A000085(j).