A293970 Number of sets of exactly eight 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.

10, 206, 1926, 13957, 85610, 476631, 2477550, 12289388, 58942808, 276126959, 1272626168, 5803545269, 26305047510, 118947441994, 538263144030, 2444159610896, 11163194878438, 51392032544011, 238939873029462, 1123916805738119, 5357138152220234, 25913264903132961

Offset

21,1

Links

Alois P. Heinz, Table of n, a(n) for n = 21..816

Formula

a(n) = [x^n y^8] 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, 9)
    end:
a:= n-> coeff(b(n$2), x, 8):
seq(a(n), n=21..45);

Crossrefs

Column k=8 of A293815.

Cf. A000085.

Sequence in context: A365177 A027014 A088746 * A356973 A356960 A364989

Adjacent sequences: A293967 A293968 A293969 * A293971 A293972 A293973

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2017

Status

approved