cp's OEIS Frontend

A293969 Number of sets of exactly seven 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 A293969 #6 Oct 20 2017 18:52:18
%S A293969 1,40,394,2766,16251,86162,426894,2021990,9290152,41829426,185965908,
%T A293969 820999576,3615595261,15941247432,70583512572,314664832674,
%U A293969 1415621796873,6439720543682,29674662921377,138736843637738,659019083032289,3184439719295586,15669157686000028
%N A293969 Number of sets of exactly seven 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 A293969 Alois P. Heinz, <a href="/A293969/b293969.txt">Table of n, a(n) for n = 17..813</a>
%F A293969 a(n) = [x^n y^7] Product_{j>=1} (1+y*x^j)^A000085(j).
%p A293969 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A293969 b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p A293969       add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 8)
%p A293969     end:
%p A293969 a:= n-> coeff(b(n$2), x, 7):
%p A293969 seq(a(n), n=17..42);
%Y A293969 Column k=7 of A293815.
%Y A293969 Cf. A000085.
%K A293969 nonn
%O A293969 17,2
%A A293969 _Alois P. Heinz_, Oct 20 2017