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 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}. 6
 1, 2, 14, 124, 1314, 15272, 187692, 2399784, 31592878, 425363952, 5830034720, 81072032060, 1140994231458, 16221323177468, 232615054822964, 3360682669655028, 48870013251334676, 714733339229024336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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] 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 EXAMPLE 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. 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 *) CROSSREFS Cf. A025591, A060005, A063865, A063867. Sequence in context: A199560 A283184 A319536 * A349261 A121082 A216595 Adjacent sequences: A060465 A060466 A060467 * A060469 A060470 A060471 KEYWORD nice,nonn AUTHOR Roland Bacher, Mar 15 2001 STATUS approved

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Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)