A293964 Number of sets of exactly two 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.

2, 5, 18, 52, 168, 533, 1792, 6161, 22088, 81690, 313224, 1239532, 5068320, 21355130, 92714368, 413915690, 1899260064, 8941932948, 43168351136, 213385326440, 1079240048256, 5578228370404, 29443746273792, 158547032884868, 870370433845888, 4866859874106392

Offset

3,1

Links

Alois P. Heinz, Table of n, a(n) for n = 3..801

Formula

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

Crossrefs

Column k=2 of A293815.

Cf. A000085.

Sequence in context: A183365 A295905 A056296 * A275079 A148417 A148418

Adjacent sequences: A293961 A293962 A293963 * A293965 A293966 A293967

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2017

Status

approved