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A179428
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Number of ways to place 8 nonattacking kings on an n X n toroidal board.
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3
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0, 0, 0, 0, 0, 486, 346381, 36285336, 956078397, 12428297150, 104000525596, 643409498286, 3191250652226, 13361641961066, 48905750870775, 160414160371552, 480243686391743, 1330654487994234, 3449609146025210, 8439769551278350, 19624142987739108, 43616849672119790, 93112709811981557, 191696927842663704, 381920049400830625, 738532765420347014, 1389708580432837752, 2550402748009811870, 4573836436177381798, 8029626473495462850
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OFFSET
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1,6
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LINKS
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FORMULA
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a(n) = 1/40320*n^2 * (n^14 -252*n^12 +27874*n^10 -1759800*n^8 +68745649*n^6 -1669136028*n^4 +23447322156*n^2 -147931524720), n>=9.
G.f.: x^6*(17728x^19 - 301964x^18 + 2573500x^17 - 13833040x^16 + 51521058x^15 - 143708688x^14 + 325486412x^13 - 629393865x^12 + 996601251x^11 - 1090603627x^10 + 426710617x^9 + 807953488x^8 - 1328885640x^7 + 262625618x^6 + 1106513030x^5 - 875387697x^4 - 386005021x^3 - 30462955x^2 - 338119x - 486)/(x-1)^17.
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MATHEMATICA
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CoefficientList[Series[x^5 (17728 x^19 - 301964 x^18 + 2573500 x^17 - 13833040 x^16 + 51521058 x^15 - 143708688 x^14 + 325486412 x^13 - 629393865 x^12 + 996601251 x^11 - 1090603627 x^10 + 426710617 x^9 + 807953488 x^8 - 1328885640 x^7 + 262625618 x^6 + 1106513030 x^5 - 875387697 x^4 - 386005021 x^3 - 30462955 x^2 - 338119 x - 486) / (x - 1)^17, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 01 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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