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

Author

Alois P. Heinz, Oct 20 2017

Keywords

• nonn

Links

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

Crossrefs

Column k=2 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, 3)
    end:
a:= n-> coeff(b(n$2), x, 2):
seq(a(n), n=3..30);

Formula

a(n) = [x^n y^2] Product_{j>=1} (1+y*x^j)^A000085(j).