

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
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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}] (* JeanFrançois 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



