cp's OEIS Frontend

A294010 Number of multisets of exactly eight 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 A294010 #4 Oct 21 2017 21:24:58
%S A294010 1,2,7,22,73,240,818,2824,10004,36242,134547,512410,2001856,8033716,
%T A294010 33106372,140223388,610090236,2727581018,12520472740,58998480846,
%U A294010 285102284159,1412080134386,7160384929556,37145667315382,196924018956010,1066012662681880
%N A294010 Number of multisets of exactly eight 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 A294010 Alois P. Heinz, <a href="/A294010/b294010.txt">Table of n, a(n) for n = 8..807</a>
%F A294010 a(n) = [x^n y^8] Product_{j>=1} 1/(1-y*x^j)^A000085(j).
%p A294010 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A294010 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n,
%p A294010       add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 9)
%p A294010     end:
%p A294010 a:= n-> coeff(b(n$2), x, 8):
%p A294010 seq(a(n), n=8..40);
%Y A294010 Column k=8 of A293808.
%Y A294010 Cf. A000085.
%K A294010 nonn
%O A294010 8,2
%A A294010 _Alois P. Heinz_, Oct 21 2017