A169888 Number of n-member subsets of 1..2n whose elements sum to a multiple of n.

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

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

a(n) ~ 2^(2*n) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 28 2023

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-François 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: A354117 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