A220467 Number of ways to place 10 nonattacking kings on an n X n board.
0, 0, 0, 0, 0, 0, 1601292, 314949564, 17143061738, 423677826986, 6210264633994, 62831788827614, 481992723228798, 2982908737810114, 15548436178142582, 70420082692285198, 283631426534134042, 1034163399690010346, 3461457325296584554, 10754832937513676198
Offset: 1
Keywords
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- V. Kotesovec, Non-attacking chess pieces
Crossrefs
Programs
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Mathematica
Rest[CoefficientList[Series[-2*x^7*(97581*x^22 - 1758956*x^21 + 16320562*x^20 - 100734462*x^19 + 443795293*x^18 - 1471049082*x^17 + 3971393292*x^16 - 9304893422*x^15 + 17917931016*x^14 - 22612415810*x^13 + 6949925614*x^12 + 21430418050*x^11 + 9738010368*x^10 - 153051533038*x^9 + 256884162558*x^8 - 71451647970*x^7 - 265785285277*x^6 + 220345759446*x^5 + 251887022384*x^4 + 63841610284*x^3 + 5432696107*x^2 + 140661216*x + 800646)/(x-1)^21, {x, 0, 20}], x]]
Formula
a(n) = n^20/3628800 - n^18/8960 + n^17/6720 + 353*n^16/17280 - 53*n^15/1008 - 29467*n^14/13440 + 11867*n^13/1440 + 25901053*n^12/172800 - 107495*n^11/144 - 8467959*n^10/1280 + 122792641*n^9/2880 + 32499630031*n^8/181440 - 112903333*n^7/72 - 16042907329*n^6/6720 + 36445613711*n^5/1008 - 1784819159*n^4/300 - 9997453897*n^3/21 + 85979117831*n^2/140 + 13635070421*n/5 - 5609601346, for n>=9.
G.f.: -2*x^7*(97581*x^22 - 1758956*x^21 + 16320562*x^20 - 100734462*x^19 + 443795293*x^18 - 1471049082*x^17 + 3971393292*x^16 - 9304893422*x^15 + 17917931016*x^14 - 22612415810*x^13 + 6949925614*x^12 + 21430418050*x^11 + 9738010368*x^10 - 153051533038*x^9 + 256884162558*x^8 - 71451647970*x^7 - 265785285277*x^6 + 220345759446*x^5 + 251887022384*x^4 + 63841610284*x^3 + 5432696107*x^2 + 140661216*x + 800646)/(x-1)^21.