A294005 - OEIS

%I #5 Oct 21 2017 21:04:55

%S 1,2,7,22,68,218,721,2438,8491,30478,112524,428382,1678600,6778708,

%T 28169286,120516092,530081370,2396797920,11125584584,52993063796,

%U 258676491628,1293160049244,6612750833996,34564483264256,184470133103464,1004514566402816

%N 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 Alois P. Heinz, <a href="/A294005/b294005.txt">Table of n, a(n) for n = 3..802</a>

%F a(n) = [x^n y^3] 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, 4)

%p     end:

%p a:= n-> coeff(b(n$2), x, 3):

%p seq(a(n), n=3..30);

%Y Column k=3 of A293808.

%Y Cf. A000085.

%K nonn

%O 3,2

%A _Alois P. Heinz_, Oct 21 2017