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%I #19 Apr 19 2022 04:38:50
%S 0,0,126,2032,20502,160696,929880,4117520,15037036,47368960,132577826,
%T 336828368,789558314,1729320120,3574328936,7027309888,13226773092,
%U 23959787480,41954706558,71276149776,117848892710,190142197976
%N Number of ways to place 5 nonattacking zebras on an n X n board.
%C Zebra is a (fairy chess) leaper [2,3].
%H Vincenzo Librandi, <a href="/A172140/b172140.txt">Table of n, a(n) for n = 1..1000</a>
%H Vaclav 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>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F a(n) = (n^10 - 90*n^8 + 400*n^7 + 2915*n^6 - 26880*n^5 + 2430*n^4 + 609920*n^3 - 1517496*n^2 - 4188480*n + 16581120)/120, n >= 12.
%F For any fixed value of k > 1, a(n) = n^(2k) /k! - 9n^(2k - 2) /2/(k - 2)! + 20n^(2k - 3) /(k - 2)! + ...
%F G.f.: 2*x^3 * (100*x^19 -648*x^18 +1450*x^17 -2126*x^16 +10452*x^15 -43872*x^14 +92798*x^13 -100834*x^12 +56460*x^11 -61636*x^10 +182288*x^9 -303224*x^8 +275038*x^7 -128982*x^6 +21681*x^5 +1933*x^4 -13072*x^3 -2540*x^2 -323*x -63) / (x-1)^11. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[2x^2(100x^19 -648x^18 +1450x^17 -2126x^16 +10452x^15 - 43872x^14 +92798x^13 -100834x^12 +56460x^11 -61636x^10 +182288x^9 -303224x^8 + 275038x^7 -128982x^6 +21681x^5 +1933x^4 -13072x^3 -2540x^2 -323x-63)/(x-1)^11, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 27 2013 *)
%o (SageMath) [0,0,126,2032,20502,160696,929880,4117520,15037036,47368960,132577826] + [(n^10 -90*n^8 +400*n^7 +2915*n^6 -26880*n^5 +2430*n^4 +609920*n^3 - 1517496*n^2 -4188480*n +16581120)/120 for n in (12..50)] # _G. C. Greubel_, Apr 19 2022
%Y Cf. A108792, A172129, A172136, A172137, A172138, A172139.
%K nonn
%O 1,3
%A _Vaclav Kotesovec_, Jan 26 2010
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