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A309187
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(1/8) times the number of n-member subsets of [8n] whose elements sum to a multiple of n.
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2
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1, 7, 85, 1127, 16451, 255619, 4141383, 69159399, 1182125128, 20581143157, 363704640476, 6506965279907, 117626432708864, 2145180354493281, 39421026305282660, 729242353169440743, 13568988503585900648, 253785064585174334488, 4768543107831461199897
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OFFSET
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1,2
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COMMENTS
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Also (1/7) times the number of n-member subsets of [8n-1] whose elements sum to a multiple of n.
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LINKS
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FORMULA
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a(n) = 1/(8n) * Sum_{d|n} binomial(8d,d)*(-1)^(n+d)*phi(n/d).
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MAPLE
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with(numtheory):
a:= n-> add(binomial(8*d, d)*(-1)^(n+d)*
phi(n/d), d in divisors(n))/(8*n):
seq(a(n), n=1..25);
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PROG
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(PARI) a(n) = 1/(8*n) * sumdiv(n, d, binomial(8*d, d)*(-1)^(n+d)*eulerphi(n/d)); \\ Michel Marcus, Jul 18 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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