Voozh

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

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

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: