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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

Alois P. Heinz, Table of n, a(n) for n = 1..806

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

Column k=7 of A309148.

Sequence in context: A230282 A186668 A025609 * A156887 A239847 A264634

Adjacent sequences:  A309183 A309184 A309185 * A309187 A309188 A309189

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 15 2019

STATUS

approved

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Last modified February 25 05:47 EST 2020. Contains 332220 sequences. (Running on oeis4.)