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%I #13 Aug 23 2017 13:00:12
%S 0,0,0,0,440,38368,1022320,14082528,126490352,837543200,4412818240,
%T 19447224864,74255991784,251997948736,774861621936,2191005028672,
%U 5764306674400,14243327787456,33309659739904,74194554880960,158241369977880,324605935279648,642894402918768
%N Number of ways to place 7 nonattacking bishops on an n X n board.
%H Vincenzo Librandi, <a href="/A187239/b187239.txt">Table of n, a(n) for n = 1..1000</a>
%H Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, <a href="http://arxiv.org/abs/1609.00853">A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks)</a>, arXiv preprint arXiv:1609.00853, a12016
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens, kings, bishops and knights</a> (in English and Czech)
%H E. Weisstein, <a href="http://mathworld.wolfram.com/BishopsProblem.html">Bishops Problem</a>, mathWorld.
%F a(n) = n^14/5040 - n^13/180 + 313n^12/4320 - 383n^11/648 + 14797n^10/4320 - 38233n^9/2520 + 3217n^8/60 - 145469n^7/945 + 1546679n^6/4320 - 4297801n^5/6480 + 257903n^4/270 - 3915679n^3/3780 + 1787007n^2/2240 - 318023n/840 + 9503/128 + (-n^8/192 + n^7/8 - 389n^6/288 + 689n^5/80 - 319n^4/9 + 1153n^3/12 - 95965n^2/576 + 20129n/120 - 9503/128)*(-1)^n.
%F G.f.: -8x^5*(630x^18 + 10620x^17 + 153525x^16 + 1211058x^15 + 6621390x^14 + 24647178x^13 + 66958554x^12 + 133891418x^11 + 202680754x^10 + 232634698x^9 + 204008900x^8 + 135332502x^7 + 67245306x^6 + 24326718x^5 + 6174582x^4 + 1024222x^3 + 99344x^2 + 4466x + 55)/((x-1)^15*(x+1)^9).
%F a(7) = A002465(7).
%t CoefficientList[Series[- 8 x^4 (630 x^18 + 10620 x^17 + 153525 x^16 + 1211058 x^15 + 6621390 x^14 + 24647178 x^13 + 66958554 x^12 + 133891418 x^11 + 202680754 x^10 + 232634698 x^9 + 204008900 x^8 + 135332502 x^7 + 67245306 x^6 + 24326718 x^5 + 6174582 x^4 + 1024222 x^3 + 99344 x^2 + 4466 x + 55) / ((x - 1)^15 (x + 1)^9), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 02 2013 *)
%Y Cf. A172123, A172124, A172127, A172129, A176886.
%K nonn,easy
%O 1,5
%A _Vaclav Kotesovec_, Mar 07 2011
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