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%I #8 Sep 12 2015 11:00:20
%S 0,0,24,926,37282,394202,2484382,10999618,38168864,110899878,
%T 281638602,643766432,1352358921,2651129458,4906381466,8648792662,
%U 14623854922,23851793294,37697787702,57953320884,86929476107,127563008202,183536011462,259410007946,360775279732
%N Number of ways to place 7 nonattacking kings on a 7 X n board.
%H Vincenzo Librandi, <a href="/A172206/b172206.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) = (117649n^7 -2873997n^6 +32197753n^5 -215350695n^4 +932130286n^3 -2618213868n^2 +4424623272n -3468569760)/720, n>=6. For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - 3(k-1)(3k-2)/2/k!*(kn)^(k-1) + ... .
%F G.f.: x^3*(3387*x^10 -13990*x^9 +57102*x^8 -55038*x^7 +217860*x^6 +137902*x^5 +324486*x^4 +120530*x^3 +30546*x^2 +734*x +24)/(x-1)^8. - _Vaclav Kotesovec_, Mar 24 2010
%t CoefficientList[Series[x^2 (3387 x^10 - 13990 x^9 + 57102 x^8 - 55038 x^7 + 217860 x^6 + 137902 x^5 + 324486 x^4 + 120530 x^3 + 30546 x^2 + 734 x + 24) / (x - 1)^8, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 27 2013 *)
%Y Cf. A061993, A172202, A172203, A172204, A172205.
%K nonn,easy
%O 1,3
%A _Vaclav Kotesovec_, Jan 29 2010