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A189791
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Number of ways to place n nonattacking bishops on an 2n x 2n toroidal board.
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3
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4, 80, 2688, 132864, 8647680, 699678720, 67711795200, 7629571031040, 981168437329920, 141817953779712000, 22760391875493888000, 4016046336733347840000, 772743693378451931136000, 161027573368536472485888000, 36127883615009765477842944000
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n)=2^n*n!*Sum[Binomial[n,i]^3,{i,0,n}].
Asymptotic: a(n) ~ 2^(4n+1)*(n-1)!/Pi/sqrt(3) ~ 2^(4n+1)*n^n/exp(n)*sqrt(2/(3*Pi*n)).
Recurrence: a(n) = ((14*n^2-14*n+4)*a(n-1) + 32*(n-1)^3*a(n-2))/n.
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MATHEMATICA
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Table[2^n*n!*Sum[Binomial[n, i]^3, {i, 0, n}], {n, 1, 20}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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