A294010 Number of multisets of exactly eight 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, 10004, 36242, 134547, 512410, 2001856, 8033716, 33106372, 140223388, 610090236, 2727581018, 12520472740, 58998480846, 285102284159, 1412080134386, 7160384929556, 37145667315382, 196924018956010, 1066012662681880

Offset

8,2

Links

Alois P. Heinz, Table of n, a(n) for n = 8..807

Formula

a(n) = [x^n y^8] 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, 9)
    end:
a:= n-> coeff(b(n$2), x, 8):
seq(a(n), n=8..40);

Crossrefs

Column k=8 of A293808.

Cf. A000085.

Sequence in context: A294007 A294008 A294009 * A294011 A294012 A293809

Adjacent sequences: A294007 A294008 A294009 * A294011 A294012 A294013

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2017

Status

approved