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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

Alois P. Heinz, Table of n, a(n) for n = 21..816

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: A041180 A027014 A088746 * A245912 A245918 A211107

Adjacent sequences:  A293967 A293968 A293969 * A293971 A293972 A293973

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 20 2017

STATUS

approved

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Last modified December 8 16:34 EST 2021. Contains 349596 sequences. (Running on oeis4.)