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%I #5 Oct 21 2017 21:17:36
%S 1,2,7,22,73,240,818,2816,9967,36080,133875,509676,1990984,7990628,
%T 32936173,139548808,607402437,2716780286,12476624346,58818236078,
%U 284350933608,1408898449946,7146679566822,37085526689402,196654885016221,1064783059174600
%N Number of multisets of exactly six 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="/A294008/b294008.txt">Table of n, a(n) for n = 6..805</a>
%F a(n) = [x^n y^6] Product_{j>=1} 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 or i=1, x^n,
%p add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 7)
%p end:
%p a:= n-> coeff(b(n$2), x, 6):
%p seq(a(n), n=6..35);
%Y Column k=6 of A293808.
%Y Cf. A000085.
%K nonn
%O 6,2
%A _Alois P. Heinz_, Oct 21 2017
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