cp's OEIS Frontend

A316410 Number of multisets of exactly nine nonempty binary words with a total of n letters such that no word has a majority of 0's.

%I A316410 #9 Jul 02 2018 16:31:58
%S A316410 1,3,10,33,98,291,826,2320,6342,17188,45684,120435,313280,808581,
%T A316410 2065885,5241557,13191343,32992806,81964072,202499115,497418503,
%U A316410 1215823396,2956890329,7159215090,17256728038,41428552721,99060756883,235997525351,560191343126
%N A316410 Number of multisets of exactly nine nonempty binary words with a total of n letters such that no word has a majority of 0's.
%H A316410 Alois P. Heinz, <a href="/A316410/b316410.txt">Table of n, a(n) for n = 9..1000</a>
%F A316410 a(n) = [x^n y^9] 1/Product_{j>=1} (1-y*x^j)^A027306(j).
%p A316410 g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
%p A316410 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
%p A316410        binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 10)
%p A316410     end:
%p A316410 a:= n-> coeff(b(n$2), x, 9):
%p A316410 seq(a(n), n=9..37);
%Y A316410 Column k=9 of A292506.
%Y A316410 Cf. A027306, A292549.
%K A316410 nonn
%O A316410 9,2
%A A316410 _Alois P. Heinz_, Jul 02 2018