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A172158 Number of ways to place 6 nonattacking kings on an n X n board. 13

%I

%S 0,0,0,0,978,62266,1220298,12033330,77784658,377818258,1492665418,

%T 5042436754,15062292834,40736208186,101489568538,235984235970,

%U 517314078210,1077720399538,2147500025914,4114538426818,7613150953522,13653752767866,23808409699242

%N Number of ways to place 6 nonattacking kings on an n X n board.

%H Vincenzo Librandi, <a href="/A172158/b172158.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^12 - 135n^10 + 180n^9 + 7465n^8 - 18840n^7 - 202665n^6 + 751860n^5 + 2442334n^4 - 13441200n^3 - 3643800n^2 + 89860320n - 108217440)/720, n>=5. For any fixed value of k > 1, a(n) = n^(2k)/k! - 9n^(2k-2)/2/(k-2)! + 6n^(2k-3)/(k-2)! ... - _Vaclav Kotesovec_, Jan 27 2010

%F G.f.: -2x^5 * (465x^12 -4432x^11 +14622x^10 -20892x^9 +36103x^8 -162056x^7 +376992x^6 -263140x^5 -287097x^4 +373248x^3 +243562x^2 +24776x +489)/(x-1)^13. - _Vaclav Kotesovec_, Mar 24 2010

%t CoefficientList[Series[-2 x^4 * (465 x^12 - 4432 x^11 + 14622 x^10 - 20892 x^9 + 36103 x^8 - 162056 x^7 + 376992 x^6 - 263140x^5 -287097 x^4 + 373248 x^3 + 243562 x^2 + 24776 x + 489) / (x - 1)^13, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 27 2013 *)

%Y Cf. A061995, A061996, A061997, A061998.

%K nonn,easy

%O 1,5

%A _Vaclav Kotesovec_, Jan 27 2010

%E More terms from _Vincenzo Librandi_, May 27 2013

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Last modified November 19 06:34 EST 2019. Contains 329310 sequences. (Running on oeis4.)