cp's OEIS Frontend

A293964 Number of sets of exactly two 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 A293964 #10 Oct 20 2017 18:48:02
%S A293964 2,5,18,52,168,533,1792,6161,22088,81690,313224,1239532,5068320,
%T A293964 21355130,92714368,413915690,1899260064,8941932948,43168351136,
%U A293964 213385326440,1079240048256,5578228370404,29443746273792,158547032884868,870370433845888,4866859874106392
%N A293964 Number of sets of exactly two 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 A293964 Alois P. Heinz, <a href="/A293964/b293964.txt">Table of n, a(n) for n = 3..801</a>
%F A293964 a(n) = [x^n y^2] Product_{j>=1} (1+y*x^j)^A000085(j).
%p A293964 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A293964 b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p A293964       add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 3)
%p A293964     end:
%p A293964 a:= n-> coeff(b(n$2), x, 2):
%p A293964 seq(a(n), n=3..30);
%Y A293964 Column k=2 of A293815.
%Y A293964 Cf. A000085.
%K A293964 nonn
%O A293964 3,1
%A A293964 _Alois P. Heinz_, Oct 20 2017