cp's OEIS Frontend

A293972 Number of sets of exactly ten 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 A293972 #6 Oct 20 2017 18:55:12
%S A293972 120,2010,21082,169846,1173098,7286181,41993502,228997683,1198101638,
%T A293972 6074435686,30073235682,146248264684,701957684114,3338454463793,
%U A293972 15784582285468,74407037119692,350575594435412,1654700449779204,7840223330719670,37363522942015498
%N A293972 Number of sets of exactly ten 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 A293972 Alois P. Heinz, <a href="/A293972/b293972.txt">Table of n, a(n) for n = 29..823</a>
%F A293972 a(n) = [x^n y^10] Product_{j>=1} (1+y*x^j)^A000085(j).
%p A293972 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A293972 b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p A293972       add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 11)
%p A293972     end:
%p A293972 a:= n-> coeff(b(n$2), x, 10):
%p A293972 seq(a(n), n=29..53);
%Y A293972 Column k=10 of A293815.
%Y A293972 Cf. A000085.
%K A293972 nonn
%O A293972 29,1
%A A293972 _Alois P. Heinz_, Oct 20 2017