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%I #6 Oct 20 2017 18:53:11
%S 10,206,1926,13957,85610,476631,2477550,12289388,58942808,276126959,
%T 1272626168,5803545269,26305047510,118947441994,538263144030,
%U 2444159610896,11163194878438,51392032544011,238939873029462,1123916805738119,5357138152220234,25913264903132961
%N 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.
%H Alois P. Heinz, <a href="/A293970/b293970.txt">Table of n, a(n) for n = 21..816</a>
%F a(n) = [x^n y^8] Product_{j>=1} (1+y*x^j)^A000085(j).
%p g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 9)
%p end:
%p a:= n-> coeff(b(n$2), x, 8):
%p seq(a(n), n=21..45);
%Y Column k=8 of A293815.
%Y Cf. A000085.
%K nonn
%O 21,1
%A _Alois P. Heinz_, Oct 20 2017
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