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%I A293965 #6 Oct 20 2017 18:48:56
%S A293965 1,8,30,114,411,1462,5237,18998,70220,265010,1024692,4059100,16504058,
%T A293965 68843340,294854550,1295771712,5843980456,27026394156,128135282356,
%U A293965 622230803212,3093321051636,15728089431744,81739630155456,433801710925696,2349410730317456
%N A293965 Number of sets of exactly three 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 A293965 Alois P. Heinz, <a href="/A293965/b293965.txt">Table of n, a(n) for n = 5..803</a>
%F A293965 a(n) = [x^n y^3] Product_{j>=1} (1+y*x^j)^A000085(j).
%p A293965 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A293965 b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p A293965       add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 4)
%p A293965     end:
%p A293965 a:= n-> coeff(b(n$2), x, 3):
%p A293965 seq(a(n), n=5..30);
%Y A293965 Column k=3 of A293815.
%Y A293965 Cf. A000085.
%K A293965 nonn
%O A293965 5,2
%A A293965 _Alois P. Heinz_, Oct 20 2017

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