A294009 Number of multisets of exactly seven 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, 73, 240, 818, 2824, 9995, 36210, 134397, 511802, 1999360, 8023808, 33066865, 140066840, 609466485, 2725084766, 12510393090, 58957378290, 284932585092, 1411369884766, 7157365741706, 37132616218394, 196866561660145, 1065754768886044

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..806

Formula

a(n) = [x^n y^7] 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, 8)
    end:
a:= n-> coeff(b(n$2), x, 7):
seq(a(n), n=7..40);

Crossrefs

Column k=7 of A293808.

Cf. A000085.

Sequence in context: A322573 A294007 A294008 * A294010 A294011 A294012

Adjacent sequences: A294006 A294007 A294008 * A294010 A294011 A294012

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2017

Status

approved