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%I #8 Oct 21 2017 20:53:10
%S 1,2,7,18,56,168,543,1792,6187,22088,81766,313224,1239764,5068320,
%T 21355894,92714368,413918310,1899260064,8941942444,43168351136,
%U 213385362136,1079240048256,5578228510556,29443746273792,158547033453372,870370433845888,4866859876496872
%N Number of multisets of exactly two 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="/A294004/b294004.txt">Table of n, a(n) for n = 2..801</a>
%F a(n) = [x^n y^2] 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, 3)
%p end:
%p a:= n-> coeff(b(n$2), x, 2):
%p seq(a(n), n=2..30);
%Y Column k=2 of A293808.
%Y Cf. A000085.
%K nonn
%O 2,2
%A _Alois P. Heinz_, Oct 21 2017
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