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A179059
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Number of non-attacking placements of 4 rooks on an n X n board.
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4
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0, 0, 0, 24, 600, 5400, 29400, 117600, 381024, 1058400, 2613600, 5880600, 12269400, 24048024, 44717400, 79497600, 135945600, 224726400, 360561024, 563376600, 859685400, 1284221400, 1881864600, 2709885024, 3840540000, 5364060000
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = 4! * binomial(n, 4)^2.
a(n) = (n^2*(-6+11*n-6*n^2+n^3)^2)/24.
G.f.: -24*x^4*(x^4 +16*x^3 +36*x^2 +16*x +1) / (x -1)^9.
(End)
Sum_{n>=4} 1/a(n) = (20*Pi^2 - 197)/9.
Sum_{n>=4} (-1)^n/a(n) = (64*log(2) - 44)/9. (End)
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MATHEMATICA
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LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 0, 0, 24, 600, 5400, 29400, 117600, 381024}, 40] (* Harvey P. Dale, Feb 19 2013 *)
a[n_] := If[n<4, 0, Coefficient[n!*LaguerreL[n, x], x, n-4] // Abs];
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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