|
|
A309186
|
|
(1/7) times the number of n-member subsets of [7n] whose elements sum to a multiple of n.
|
|
2
|
|
|
1, 6, 64, 734, 9276, 124872, 1753074, 25366334, 375677659, 5667202856, 86775157140, 1345153548200, 21069043965984, 332927798516620, 5301031234085664, 84967018635587774, 1369846562874360887, 22199151535757780226, 361411377745122110422, 5908312923795257322184
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Also (1/6) times the number of n-member subsets of [7n-1] whose elements sum to a multiple of n.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 1/(7n) * Sum_{d|n} binomial(7d,d)*(-1)^(n+d)*phi(n/d).
|
|
MAPLE
|
with(numtheory):
a:= n-> add(binomial(7*d, d)*(-1)^(n+d)*
phi(n/d), d in divisors(n))/(7*n):
seq(a(n), n=1..25);
|
|
PROG
|
(PARI) a(n) = 1/(7*n) * sumdiv(n, d, binomial(7*d, d)*(-1)^(n+d)*eulerphi(n/d)); \\ Michel Marcus, Jul 18 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|