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A060468
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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}.
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6
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1, 2, 14, 124, 1314, 15272, 187692, 2399784, 31592878, 425363952, 5830034720, 81072032060, 1140994231458, 16221323177468, 232615054822964, 3360682669655028, 48870013251334676, 714733339229024336
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = coefficient of q^0 in Product_{k=1..4*n} (q^(-k) + q^k).
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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STATUS
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approved
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