A293965 Number of sets of exactly three 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, 8, 30, 114, 411, 1462, 5237, 18998, 70220, 265010, 1024692, 4059100, 16504058, 68843340, 294854550, 1295771712, 5843980456, 27026394156, 128135282356, 622230803212, 3093321051636, 15728089431744, 81739630155456, 433801710925696, 2349410730317456

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..803

Formula

a(n) = [x^n y^3] 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, 4)
    end:
a:= n-> coeff(b(n$2), x, 3):
seq(a(n), n=5..30);

Crossrefs

Column k=3 of A293815.

Cf. A000085.

Sequence in context: A050477 A239612 A055737 * A161222 A229374 A215471

Adjacent sequences: A293962 A293963 A293964 * A293966 A293967 A293968

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2017

Status

approved