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%I #12 Jun 20 2017 22:37:01
%S 0,0,0,0,1,3600,2882737,229095676,6655170642,103395053720,
%T 1051588999820,7878155295948,46838274976147,232322652402464,
%U 995789500001315,3784235129731708,12999197522073908,40969826999523768,119876498636101786,328726265508168780,851369417500529061
%N Number of ways to place 9 nonattacking kings on an n X n board.
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>
%F Explicit formula (_Vaclav Kotesovec_, after values computed by _Andrew Woods_, Dec 04 2011): n^18/362880 - n^16/1120 + n^15/840 + 1559*n^14/12096 - 119*n^13/360 - 7681*n^12/720 + 479*n^11/12 + 9383677*n^10/17280 - 195031*n^9/72 - 24176483*n^8/1440 + 4447749*n^7/40 + 5032857271*n^6/18144 - 495178813*n^5/180 - 2551293629*n^4/2520 + 1588223225*n^3/42 - 11469403819*n^2/315 - 664490248*n/3 + 405670140, n>=8.
%F G.f.: x^5*(54764*x^21 - 805588*x^20 + 6061268*x^19 - 31485512*x^18 + 117971558*x^17 - 312791986*x^16 + 620038858*x^15 - 1193322246*x^14 + 2685590901*x^13 - 4918483903*x^12 + 3824558880*x^11 + 5110355848*x^10 - 13987162841*x^9 + 5213745395*x^8 + 15789867458*x^7 - 14255103822*x^6 - 13342741937*x^5 - 2791816301*x^4 - 174938304*x^3 - 2814508*x^2 - 3581*x - 1)/(x-1)^19.
%Y Cf. A061995, A061996, A061997, A061998, A172158, A193580, A194788, A201369.
%K nonn
%O 1,6
%A _Vaclav Kotesovec_, Dec 04 2011
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