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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.
2
1, 3, 10, 33, 98, 291, 826, 2320, 6297, 16989, 44828, 117352, 302429, 773496, 1954845, 4905939, 12195457, 30123762, 73825711, 179891662, 435427632, 1048510795, 2510267189, 5981859208, 14182293004, 33482368279, 78690956088, 184229429914, 429570180998
OFFSET
7,2
LINKS
FORMULA
a(n) = [x^n y^7] 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, 8)
end:
a:= n-> coeff(b(n$2), x, 7):
seq(a(n), n=7..35);
CROSSREFS
Column k=7 of A292506.
Sequence in context: A316405 A316406 A316407 * A316409 A316410 A316411
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 02 2018
STATUS
approved