cp's OEIS Frontend

A316408 Number of multisets of exactly seven nonempty binary words with a total of n letters such that no word has a majority of 0's.

%I A316408 #9 Jul 02 2018 16:31:13
%S A316408 1,3,10,33,98,291,826,2320,6297,16989,44828,117352,302429,773496,
%T A316408 1954845,4905939,12195457,30123762,73825711,179891662,435427632,
%U A316408 1048510795,2510267189,5981859208,14182293004,33482368279,78690956088,184229429914,429570180998
%N A316408 Number of multisets of exactly seven nonempty binary words with a total of n letters such that no word has a majority of 0's.
%H A316408 Alois P. Heinz, <a href="/A316408/b316408.txt">Table of n, a(n) for n = 7..1000</a>
%F A316408 a(n) = [x^n y^7] 1/Product_{j>=1} (1-y*x^j)^A027306(j).
%p A316408 g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
%p A316408 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
%p A316408        binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 8)
%p A316408     end:
%p A316408 a:= n-> coeff(b(n$2), x, 7):
%p A316408 seq(a(n), n=7..35);
%Y A316408 Column k=7 of A292506.
%Y A316408 Cf. A027306, A292549.
%K A316408 nonn
%O A316408 7,2
%A A316408 _Alois P. Heinz_, Jul 02 2018