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%I #9 Jul 02 2018 16:31:35
%S 1,3,10,33,98,291,826,2320,6342,17133,45504,119580,310416,798196,
%T 2033289,5136803,12878647,32056022,79277444,194822462,476101571,
%U 1156995495,2797803485,6731961588,16126628466,38459836055,91355046531,216126089962,509445131238
%N Number of multisets of exactly eight nonempty binary words with a total of n letters such that no word has a majority of 0's.
%H Alois P. Heinz, <a href="/A316409/b316409.txt">Table of n, a(n) for n = 8..1000</a>
%F a(n) = [x^n y^8] 1/Product_{j>=1} (1-y*x^j)^A027306(j).
%p g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
%p b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
%p binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 9)
%p end:
%p a:= n-> coeff(b(n$2), x, 8):
%p seq(a(n), n=8..36);
%Y Column k=8 of A292506.
%Y Cf. A027306, A292549.
%K nonn
%O 8,2
%A _Alois P. Heinz_, Jul 02 2018
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