A294005 Number of multisets 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, 2, 7, 22, 68, 218, 721, 2438, 8491, 30478, 112524, 428382, 1678600, 6778708, 28169286, 120516092, 530081370, 2396797920, 11125584584, 52993063796, 258676491628, 1293160049244, 6612750833996, 34564483264256, 184470133103464, 1004514566402816

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..802

Formula

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

Crossrefs

Column k=3 of A293808.

Cf. A000085.

Sequence in context: A308113 A291012 A369314 * A333494 A292399 A094618

Adjacent sequences: A294002 A294003 A294004 * A294006 A294007 A294008

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2017

Status

approved