cp's OEIS Frontend

A293968 Number of sets of exactly six 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 A293968 #6 Oct 20 2017 18:51:27
%S A293968 4,62,417,2414,12190,57686,260349,1143710,4936266,21117128,90035798,
%T A293968 384416432,1649398948,7133455202,31173583589,137947781614,
%U A293968 619247938106,2824375268432,13105785174035,61940904739132,298438345898409,1466892183248186,7358885205363735
%N A293968 Number of sets of exactly six 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 A293968 Alois P. Heinz, <a href="/A293968/b293968.txt">Table of n, a(n) for n = 14..810</a>
%F A293968 a(n) = [x^n y^6] Product_{j>=1} (1+y*x^j)^A000085(j).
%p A293968 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A293968 b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p A293968       add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 7)
%p A293968     end:
%p A293968 a:= n-> coeff(b(n$2), x, 6):
%p A293968 seq(a(n), n=14..40);
%Y A293968 Column k=6 of A293815.
%Y A293968 Cf. A000085.
%K A293968 nonn
%O A293968 14,1
%A A293968 _Alois P. Heinz_, Oct 20 2017