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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 19 18:30 EST 2019. Contains 320327 sequences. (Running on oeis4.)