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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.
2
1, 3, 10, 33, 98, 291, 798, 2200, 5804, 15275, 39014, 99214, 247065, 612090, 1492837, 3622213, 8682565, 20711303, 48923317, 115048586, 268374750, 623503251, 1438753371, 3307821910, 7560955644, 17225642730, 39047321794, 88249150462, 198572820286, 445610719629
OFFSET
5,2
LINKS
FORMULA
a(n) = [x^n y^5] 1/Product_{j>=1} (1-y*x^j)^A027306(j).
MAPLE
g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 6)
end:
a:= n-> coeff(b(n$2), x, 5):
seq(a(n), n=5..34);
CROSSREFS
Column k=5 of A292506.
Sequence in context: A316404 A333027 A316405 * A316407 A316408 A316409
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 02 2018
STATUS
approved