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%I #16 Sep 12 2015 11:00:23
%S 0,0,0,170,13384,257318,2774728,20202298,110018552,481719518,
%T 1781124856,5756568738,16676946372,44127887910,108192675468,
%U 248568720338,539925974784,1116836380926,2212958151968,4220919779218
%N Number of ways to place 6 nonattacking knights on an n X n board.
%H Vincenzo Librandi, <a href="/A178499/b178499.txt">Table of n, a(n) for n = 1..1000</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013
%F Explicit formula: a(n) = n^12/720-(3*n^10)/16+n^9/2+(1553*n^8)/144-(163*n^7)/3-(4493*n^6)/16+(4721*n^5)/2+(578777*n^4)/360-(143156*n^3)/3+(124917*n^2)/2+374990*n-899982, n >= 10.
%F G.f.: -2*x^4 * (200*x^18 -1540*x^17 +2602*x^16 +15442*x^15 -98586*x^14 +256698*x^13 -336146*x^12 +70977*x^11 +587107*x^10 -1302115*x^9 +1569905*x^8 -1100786*x^7 +367130*x^6 -212358*x^5 +247682*x^4 +212463*x^3 +48293*x^2 +5587*x +85) / (x-1)^13.
%t CoefficientList[Series[- 2 x^3 (200 x^18 - 1540 x^17 + 2602 x^16 + 15442 x^15 - 98586 x^14 + 256698 x^13 - 336146 x^12 + 70977 x^11 + 587107 x^10 - 1302115 x^9 + 1569905 x^8 - 1100786 x^7 + 367130 x^6 - 212358 x^5 + 247682 x^4 + 212463 x^3 + 48293 x^2 + 5587 x + 85) / (x - 1)^13, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 31 2013 *)
%Y Cf. A172132, A172134, A172135, A172136.
%Y Column k=6 of A244081.
%K nonn,easy
%O 1,4
%A _Vaclav Kotesovec_, May 28 2010
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