cp's OEIS Frontend

A316406 Number of multisets of exactly five nonempty binary words with a total of n letters such that no word has a majority of 0's.

%I A316406 #9 Jul 02 2018 16:30:32
%S A316406 1,3,10,33,98,291,798,2200,5804,15275,39014,99214,247065,612090,
%T A316406 1492837,3622213,8682565,20711303,48923317,115048586,268374750,
%U A316406 623503251,1438753371,3307821910,7560955644,17225642730,39047321794,88249150462,198572820286,445610719629
%N A316406 Number of multisets of exactly five nonempty binary words with a total of n letters such that no word has a majority of 0's.
%H A316406 Alois P. Heinz, <a href="/A316406/b316406.txt">Table of n, a(n) for n = 5..1000</a>
%F A316406 a(n) = [x^n y^5] 1/Product_{j>=1} (1-y*x^j)^A027306(j).
%p A316406 g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
%p A316406 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
%p A316406        binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 6)
%p A316406     end:
%p A316406 a:= n-> coeff(b(n$2), x, 5):
%p A316406 seq(a(n), n=5..34);
%Y A316406 Column k=5 of A292506.
%Y A316406 Cf. A027306, A292549.
%K A316406 nonn
%O A316406 5,2
%A A316406 _Alois P. Heinz_, Jul 02 2018