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Number of ways to place 8 nonattacking kings on an 8 X n board.
1

%I #13 May 11 2017 17:16:26

%S 0,0,25,1847,162531,2501726,21243084,119138166,502726650,1724809105,

%T 5059647669,13132889249,30905051345,67124176002,136380034610,

%U 261909043488,479315827404,841394145399,1424246670499,2334919892115

%N Number of ways to place 8 nonattacking kings on an 8 X n board.

%H Vincenzo Librandi, <a href="/A172261/b172261.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) = (1048576n^8 -30277632n^7 +406210560n^6 -3319585920n^5 +18136811049n^4 -68048382318n^3 +171628664735n^2 -266425935930n +194935658400)/2520, n>=7.

%F G.f.: -x^3*(11814*x^12 -80082*x^11 +366204*x^10 -759794*x^9 +1916625*x^8 -283007*x^7 +5337480*x^6 +4589514*x^5 +4426668*x^4 +1103339*x^3 +146808*x^2 +1622*x +25)/(x-1)^9. [_Vaclav Kotesovec_, Mar 24 2010]

%t CoefficientList[Series[- x^2 (11814 x^12 - 80082 x^11 + 366204 x^10 - 759794 x^9 + 1916625 x^8 - 283007 x^7 + 5337480 x^6 + 4589514 x^5 + 4426668 x^4 + 1103339 x^3 + 146808 x^2 + 1622 x + 25) / (x - 1)^9, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 29 2013 *)

%Y Cf. A172202, A172203, A172204, A172205, A172206.

%K nonn,easy

%O 1,3

%A _Vaclav Kotesovec_, Jan 30 2010