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A169888 Number of n-member subsets of 1..2n whose elements sum to a multiple of n. 8
1, 2, 2, 8, 18, 52, 152, 492, 1618, 5408, 18452, 64132, 225432, 800048, 2865228, 10341208, 37568338, 137270956, 504171584, 1860277044, 6892335668, 25631327688, 95640829924, 357975249028, 1343650267288, 5056424257552, 19073789328752, 72108867620204 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is twice A145855 (for n>0), which is the main entry for this problem.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1669

FORMULA

a(n) = A061865(2n,n). - Alois P. Heinz, Aug 28 2018

MAPLE

with(combinat): t0:=[]; for n from 1 to 8 do ans:=0; t1:=choose(2*n, n); for i in t1 do s1:=add(i[j], j=1..n); if s1 mod n = 0 then ans:=ans+1; fi; od: t0:=[op(t0), ans]; od:

MATHEMATICA

a[n_] := Sum[(-1)^(n+d)*EulerPhi[n/d]*Binomial[2d, d]/n, {d, Divisors[n]}]; Table[a[n], {n, 1, 26}] (* Jean-Fran├žois Alcover, Oct 22 2012, after T. D. Noe's program in A145855 *)

PROG

(PARI) a(n) = if(n==0, 1, sumdiv(n, d, (-1)^(n+d)*eulerphi(n/d)*binomial(2*d, d)/n)); \\ Altug Alkan, Aug 27 2018, after T. D. Noe at A145855

CROSSREFS

Cf. A061865, A119358, A145855, A318431, A318432, A318433.

Column k=2 of A304482.

Sequence in context: A053098 A194588 A175395 * A168506 A208966 A067640

Adjacent sequences:  A169885 A169886 A169887 * A169889 A169890 A169891

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 07 2010, based on a letter from Jean-Claude Babois.

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Aug 26 2018

STATUS

approved

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Last modified February 18 20:04 EST 2019. Contains 320262 sequences. (Running on oeis4.)