cp's OEIS Frontend

A294007 Number of multisets 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 A294007 #4 Oct 21 2017 21:14:05
%S A294007 1,2,7,22,73,240,811,2792,9857,35644,132119,502832,1964131,7885792,
%T A294007 32523695,137915764,600865387,2690302074,12367812720,58364059306,
%U A294007 282421855885,1400551909446,7109841300492,36919536804334,195890584265442,1061185175436116
%N A294007 Number of multisets 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 A294007 Alois P. Heinz, <a href="/A294007/b294007.txt">Table of n, a(n) for n = 5..804</a>
%F A294007 a(n) = [x^n y^5] Product_{j>=1} 1/(1-y*x^j)^A000085(j).
%p A294007 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A294007 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n,
%p A294007       add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 6)
%p A294007     end:
%p A294007 a:= n-> coeff(b(n$2), x, 5):
%p A294007 seq(a(n), n=5..35);
%Y A294007 Column k=5 of A293808.
%Y A294007 Cf. A000085.
%K A294007 nonn
%O A294007 5,2
%A A294007 _Alois P. Heinz_, Oct 21 2017