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%I #15 Sep 12 2015 11:00:24
%S 0,0,0,0,0,486,346381,36285336,956078397,12428297150,104000525596,
%T 643409498286,3191250652226,13361641961066,48905750870775,
%U 160414160371552,480243686391743,1330654487994234,3449609146025210,8439769551278350,19624142987739108,43616849672119790,93112709811981557,191696927842663704,381920049400830625,738532765420347014,1389708580432837752,2550402748009811870,4573836436177381798,8029626473495462850
%N Number of ways to place 8 nonattacking kings on an n X n toroidal board.
%H Vincenzo Librandi, <a href="/A179428/b179428.txt">Table of n, a(n) for n = 1..1000</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a>
%F 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.
%F 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.
%t 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 *)
%Y Cf. A179403, A179404, A179424, A179425, A179426, A179427.
%K nonn,easy
%O 1,6
%A _Vaclav Kotesovec_, Jan 07 2011
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