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A309188 (1/9) times the number of n-member subsets of [9n] whose elements sum to a multiple of n. 2
1, 8, 109, 1640, 27151, 478232, 8782075, 166237160, 3220837534, 63562714008, 1273237637706, 25820645555000, 529080420540114, 10937268134114568, 227824992158991334, 4777204094770874856, 100757627271124231383, 2136117417345649876112, 45496022230420668679932 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also (1/8) times the number of n-member subsets of [9n-1] whose elements sum to a multiple of n.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..737

FORMULA

a(n) = 1/(9n) * Sum_{d|n} binomial(9d,d)*(-1)^(n+d)*phi(n/d).

MAPLE

with(numtheory):

a:= n-> add(binomial(9*d, d)*(-1)^(n+d)*

        phi(n/d), d in divisors(n))/(9*n):

seq(a(n), n=1..25);

PROG

(PARI) a(n) = 1/(9*n) * sumdiv(n, d, binomial(9*d, d)*(-1)^(n+d)*eulerphi(n/d)); \\ Michel Marcus, Jul 19 2019

CROSSREFS

Column k=9 of A309148.

Sequence in context: A095917 A259233 A322718 * A098623 A297971 A076151

Adjacent sequences:  A309185 A309186 A309187 * A309189 A309190 A309191

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 15 2019

STATUS

approved

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Last modified July 31 23:01 EDT 2021. Contains 346377 sequences. (Running on oeis4.)