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%I A294011 #4 Oct 21 2017 21:28:22
%S A294011 1,2,7,22,73,240,818,2824,10004,36252,134583,512580,2002550,8036582,
%T A294011 33117812,140269222,610272640,2728310488,12523401416,59010337316,
%U A294011 285150731417,1412280452528,7161224109072,37149235934192,196939443174176,1066080526789082
%N A294011 Number of multisets of exactly nine 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 A294011 Alois P. Heinz, <a href="/A294011/b294011.txt">Table of n, a(n) for n = 9..808</a>
%F A294011 a(n) = [x^n y^9] Product_{j>=1} 1/(1-y*x^j)^A000085(j).
%p A294011 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A294011 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n,
%p A294011       add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 10)
%p A294011     end:
%p A294011 a:= n-> coeff(b(n$2), x, 9):
%p A294011 seq(a(n), n=9..40);
%Y A294011 Column k=9 of A293808.
%Y A294011 Cf. A000085.
%K A294011 nonn
%O A294011 9,2
%A A294011 _Alois P. Heinz_, Oct 21 2017

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