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%I #16 Feb 18 2018 15:03:31
%S 1,78,1758,38588,383246,2135344,8891854,30108310,86669806,219845764,
%T 504261973,1065642840,2104251027,3924818982,6973786593,11884673662,
%U 19532410762,31097451768,48140491605,72688612756,107333684073
%N Number of ways to place 7 nonattacking knights on a 7 X n board.
%H Vincenzo Librandi, <a href="/A172217/b172217.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^7-2571471n^6+29223943n^5-216954465n^4+1114503256n^3-3907492824n^2+8562799512n-8962924320)/720,n>=12.
%F For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - 3(k-1)(3k-4)/2/k!*(kn)^(k-1) + ...
%F G.f.: x * (252*x^18 -272*x^17 -5134*x^16 +14468*x^15 +19721*x^14 -132666*x^13 +174233*x^12 +119440*x^11 -540473*x^10 +654954*x^9 -89133*x^8 -93778*x^7 +497782*x^6 +56796*x^5 +119468*x^4 +26652*x^3 +1162*x^2 +70*x +1) / (x-1)^8. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[(252 x^18 - 272 x^17 - 5134 x^16 + 14468 x^15 + 19721 x^14 - 132666 x^13 + 174233 x^12 + 119440 x^11 - 540473 x^10 + 654954 x^9 - 89133 x^8 - 93778 x^7 + 497782 x^6 + 56796 x^5 + 119468 x^4 + 26652 x^3 + 1162 x^2 + 70 x + 1) / (x - 1)^8, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 27 2013 *)
%Y Cf. A061993, A172212, A172213, A172214, A172215.
%K nonn,easy
%O 1,2
%A _Vaclav Kotesovec_, Jan 29 2010
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