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A293970 Number of sets 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. 2
10, 206, 1926, 13957, 85610, 476631, 2477550, 12289388, 58942808, 276126959, 1272626168, 5803545269, 26305047510, 118947441994, 538263144030, 2444159610896, 11163194878438, 51392032544011, 238939873029462, 1123916805738119, 5357138152220234, 25913264903132961 (list; graph; refs; listen; history; text; internal format)
OFFSET
21,1
LINKS
FORMULA
a(n) = [x^n y^8] Product_{j>=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, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 9)
end:
a:= n-> coeff(b(n$2), x, 8):
seq(a(n), n=21..45);
CROSSREFS
Column k=8 of A293815.
Cf. A000085.
Sequence in context: A365177 A027014 A088746 * A356973 A356960 A364989
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 20 2017
STATUS
approved

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Last modified February 24 22:04 EST 2024. Contains 370307 sequences. (Running on oeis4.)