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%I #12 Feb 20 2018 14:27:11
%S 0,0,0,128,120,30312,283906,1872064,8643186,31702920,98179400,
%T 267487920,659015500,1496908840,3179369070,6382030592,12207535134,
%U 22396355496,39617305308,67860021680
%N Number of ways to place 5 nonattacking knights on an n X n toroidal board.
%H Vincenzo Librandi, <a href="/A172532/b172532.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) = n^2*(n^8 - 90*n^6 + 3395*n^4 - 64290*n^2 + 522504)/120, n>=10.
%F G.f.: -2*x^4*(648*x^16-10328*x^15+71820*x^14-295572*x^13+818512*x^12-1640088*x^11+2492742*x^10-2967118*x^9+2825821*x^8-2185007*x^7+1376780*x^6-677852*x^5+219349*x^4-32023*x^3+18016*x^2-644*x+64)/(x-1)^11. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[- 2 x^3 (648 x^16 - 10328 x^15 + 71820 x^14 - 295572 x^13 + 818512 x^12 - 1640088 x^11 + 2492742 x^10 - 2967118 x^9 + 2825821 x^8 - 2185007 x^7 + 1376780 x^6 - 677852 x^5 + 219349 x^4 - 32023 x^3 + 18016 x^2 - 644 x + 64) / (x - 1)^11, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 29 2013 *)
%Y Cf. A172529, A172530, A172531, A172136.
%K nonn,easy
%O 1,4
%A _Vaclav Kotesovec_, Feb 06 2010
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