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

17,2

Links

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

Formula

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

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);

Crossrefs

Column k=7 of A293815.

Cf. A000085.

Sequence in context: A221820 A301528 A253132 * A168192 A251129 A007772

Adjacent sequences: A293966 A293967 A293968 * A293970 A293971 A293972

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2017

Status

approved