cp's OEIS Frontend

A293966 Number of sets 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.

%I A293966 #6 Oct 20 2017 18:49:46
%S A293966 4,22,116,482,1966,7682,29845,115438,449870,1770788,7073065,28727652,
%T A293966 118907910,502249944,2167410896,9563204836,43166853057,199391604156,
%U A293966 942578850020,4559743209208,22566589645408,114215149597312,590875202641724,3122678708581528
%N A293966 Number of sets 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 A293966 Alois P. Heinz, <a href="/A293966/b293966.txt">Table of n, a(n) for n = 8..805</a>
%F A293966 a(n) = [x^n y^4] Product_{j>=1} (1+y*x^j)^A000085(j).
%p A293966 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A293966 b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p A293966       add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 5)
%p A293966     end:
%p A293966 a:= n-> coeff(b(n$2), x, 4):
%p A293966 seq(a(n), n=8..33);
%Y A293966 Column k=4 of A293815.
%Y A293966 Cf. A000085.
%K A293966 nonn
%O A293966 8,1
%A A293966 _Alois P. Heinz_, Oct 20 2017