cp's OEIS Frontend

A293967 Number of sets of exactly five 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 A293967 #6 Oct 20 2017 18:50:35
%S A293967 6,48,274,1338,6035,25874,108002,444458,1818905,7451418,30693022,
%T A293967 127604480,536876960,2291507552,9939572897,43885543586,197465168488,
%U A293967 906430558822,4247727231198,20333276583188,99450038211268,497066503157976,2538584563166367
%N A293967 Number of sets of exactly five 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 A293967 Alois P. Heinz, <a href="/A293967/b293967.txt">Table of n, a(n) for n = 11..807</a>
%F A293967 a(n) = [x^n y^5] Product_{j>=1} (1+y*x^j)^A000085(j).
%p A293967 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A293967 b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p A293967       add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 6)
%p A293967     end:
%p A293967 a:= n-> coeff(b(n$2), x, 5):
%p A293967 seq(a(n), n=11..35);
%Y A293967 Column k=5 of A293815.
%Y A293967 Cf. A000085.
%K A293967 nonn
%O A293967 11,1
%A A293967 _Alois P. Heinz_, Oct 20 2017