cp's OEIS Frontend

A294004 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.

%I A294004 #8 Oct 21 2017 20:53:10
%S A294004 1,2,7,18,56,168,543,1792,6187,22088,81766,313224,1239764,5068320,
%T A294004 21355894,92714368,413918310,1899260064,8941942444,43168351136,
%U A294004 213385362136,1079240048256,5578228510556,29443746273792,158547033453372,870370433845888,4866859876496872
%N A294004 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 A294004 Alois P. Heinz, <a href="/A294004/b294004.txt">Table of n, a(n) for n = 2..801</a>
%F A294004 a(n) = [x^n y^2] Product_{j>=1} 1/(1-y*x^j)^A000085(j).
%p A294004 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A294004 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n,
%p A294004       add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 3)
%p A294004     end:
%p A294004 a:= n-> coeff(b(n$2), x, 2):
%p A294004 seq(a(n), n=2..30);
%Y A294004 Column k=2 of A293808.
%Y A294004 Cf. A000085.
%K A294004 nonn
%O A294004 2,2
%A A294004 _Alois P. Heinz_, Oct 21 2017