cp's OEIS Frontend

A294005 Number of multisets 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.

%I A294005 #5 Oct 21 2017 21:04:55
%S A294005 1,2,7,22,68,218,721,2438,8491,30478,112524,428382,1678600,6778708,
%T A294005 28169286,120516092,530081370,2396797920,11125584584,52993063796,
%U A294005 258676491628,1293160049244,6612750833996,34564483264256,184470133103464,1004514566402816
%N A294005 Number of multisets 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 A294005 Alois P. Heinz, <a href="/A294005/b294005.txt">Table of n, a(n) for n = 3..802</a>
%F A294005 a(n) = [x^n y^3] Product_{j>=1} 1/(1-y*x^j)^A000085(j).
%p A294005 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A294005 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n,
%p A294005       add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 4)
%p A294005     end:
%p A294005 a:= n-> coeff(b(n$2), x, 3):
%p A294005 seq(a(n), n=3..30);
%Y A294005 Column k=3 of A293808.
%Y A294005 Cf. A000085.
%K A294005 nonn
%O A294005 3,2
%A A294005 _Alois P. Heinz_, Oct 21 2017