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%I #6 Oct 20 2017 18:54:19
%S 45,740,7265,54844,355786,2086218,11402599,59244154,296592681,
%T 1444795518,6898985716,32478508414,151439118998,702039301562,
%U 3246061184641,15011635714770,69604533115983,324297338323040,1521325113273431,7199243859471728,34426802099939524
%N Number of sets of exactly nine 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="/A293971/b293971.txt">Table of n, a(n) for n = 25..820</a>
%F a(n) = [x^n y^9] 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, 10)
%p end:
%p a:= n-> coeff(b(n$2), x, 9):
%p seq(a(n), n=25..49);
%Y Column k=9 of A293815.
%Y Cf. A000085.
%K nonn
%O 25,1
%A _Alois P. Heinz_, Oct 20 2017
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