A060468 Number of fair distributions (equal sum) of the integers {1,..,4n} between A and B = number of solutions to the equation {+-1 +-2 +- 3 ... +-4*n = 0}.

1, 2, 14, 124, 1314, 15272, 187692, 2399784, 31592878, 425363952, 5830034720, 81072032060, 1140994231458, 16221323177468, 232615054822964, 3360682669655028, 48870013251334676, 714733339229024336

Offset: 0

Author

Roland Bacher, Mar 15 2001

Keywords

• nice
• nonn

Examples

			a(1)=2: give either the set {1,4} to A and {2,3} to B or give {2,3} to A and {1,4} to B.
		

Links

• Ray Chandler, Table of n, a(n) for n = 0..834 (terms < 10^1000)
• Steven R. Finch, Signum equations and extremal coefficients, February 7, 2009. [Cached copy, with permission of the author]

Crossrefs

Cf. A025591, A060005, A063865, A063867.

Programs

Mathematica

a[n_] := Coefficient[Product[q^(-k) + q^k, {k, 1, 4*n}], q, 0]; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Sep 26 2013 *)

Formula

a(n) = coefficient of q^0 in Product_{k=1..4*n} (q^(-k) + q^k).

a(n) = A025591(4n) = A063865(4n) = A063867(4n) = 2*A060005(n). Seems to be close to sqrt(3/32Pi)*16^n/sqrt(n^3 + n^2*0.6 + n*0.1385...) and sqrt(n*Pi/2)*A063074(n). - Henry Bottomley, Jul 30 2005