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A309183 (1/4) times the number of n-member subsets of [4n] whose elements sum to a multiple of n. 2
1, 3, 19, 115, 776, 5601, 42288, 328755, 2615104, 21191128, 174303163, 1451430673, 12211799224, 103655906784, 886568153744, 7633233556275, 66105170315084, 575445689884848, 5032380942945322, 44191451788247640, 389514699013012242, 3444925385161998521 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also (1/3) times the number of n-member subsets of [4n-1] whose elements sum to a multiple of n.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = 1/(4n) * Sum_{d|n} binomial(4d,d)*(-1)^(n+d)*phi(n/d).

MAPLE

with(numtheory):

a:= n-> add(binomial(4*d, d)*(-1)^(n+d)*

        phi(n/d), d in divisors(n))/(4*n):

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

CROSSREFS

Column k=4 of A309148.

Sequence in context: A116979 A267802 A229928 * A261777 A037781 A037585

Adjacent sequences:  A309180 A309181 A309182 * A309184 A309185 A309186

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 15 2019

STATUS

approved

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Last modified August 1 22:01 EDT 2021. Contains 346408 sequences. (Running on oeis4.)