A294004 Number of multisets 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.

1, 2, 7, 18, 56, 168, 543, 1792, 6187, 22088, 81766, 313224, 1239764, 5068320, 21355894, 92714368, 413918310, 1899260064, 8941942444, 43168351136, 213385362136, 1079240048256, 5578228510556, 29443746273792, 158547033453372, 870370433845888, 4866859876496872

Offset

2,2

Links

Alois P. Heinz, Table of n, a(n) for n = 2..801

Formula

a(n) = [x^n y^2] Product_{j>=1} 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 or i=1, x^n,
      add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 3)
    end:
a:= n-> coeff(b(n$2), x, 2):
seq(a(n), n=2..30);

Crossrefs

Column k=2 of A293808.

Cf. A000085.

Sequence in context: A046672 A046866 A291255 * A214836 A176813 A000988

Adjacent sequences: A294001 A294002 A294003 * A294005 A294006 A294007

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2017

Status

approved