%I #4 Oct 21 2017 21:10:24

%S 1,2,7,22,73,234,791,2702,9507,34258,126807,482306,1885031,7578028,

%T 31316391,133117500,581531653,2611112712,12037781812,56962049532,

%U 276345797775,1373655295948,6988160240848,36356528106984,193225799686632,1048279646446240

%N Number of multisets of exactly four 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="/A294006/b294006.txt">Table of n, a(n) for n = 4..803</a>

%F a(n) = [x^n y^4] 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, 5)

%p end:

%p a:= n-> coeff(b(n$2), x, 4):

%p seq(a(n), n=4..35);

%Y Column k=4 of A293808.

%Y Cf. A000085.

%K nonn

%O 4,2

%A _Alois P. Heinz_, Oct 21 2017