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A309187
(1/8) times the number of n-member subsets of [8n] whose elements sum to a multiple of n.
2
1, 7, 85, 1127, 16451, 255619, 4141383, 69159399, 1182125128, 20581143157, 363704640476, 6506965279907, 117626432708864, 2145180354493281, 39421026305282660, 729242353169440743, 13568988503585900648, 253785064585174334488, 4768543107831461199897
OFFSET
1,2
COMMENTS
Also (1/7) times the number of n-member subsets of [8n-1] whose elements sum to a multiple of n.
LINKS
FORMULA
a(n) = 1/(8n) * Sum_{d|n} binomial(8d,d)*(-1)^(n+d)*phi(n/d).
MAPLE
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);
PROG
(PARI) a(n) = 1/(8*n) * sumdiv(n, d, binomial(8*d, d)*(-1)^(n+d)*eulerphi(n/d)); \\ Michel Marcus, Jul 18 2019
CROSSREFS
Column k=8 of A309148.
Sequence in context: A155631 A126344 A193578 * A026001 A371363 A064089
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 15 2019
STATUS
approved