This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A187240 #17 Feb 16 2025 08:33:14
%S A187240 0,0,0,0,32,12944,867328,22522960,328097824,3209594096,23460698496,
%T A187240 137045115696,670158151296,2835083100640,10634260782464,
%U A187240 36033282628832,111923478184128,322412415716896,869530617762304,2212626780591008,5346773160475488,12336574243905648,27303885052866048
%N A187240 Number of ways to place 8 nonattacking bishops on an n X n board.
%H A187240 Vincenzo Librandi, <a href="/A187240/b187240.txt">Table of n, a(n) for n = 1..1000</a>
%H A187240 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 A187240 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 A187240 E. Weisstein, <a href="https://mathworld.wolfram.com/BishopsProblem.html">Bishops Problem</a>, MathWorld
%H A187240 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (6, -4, -46, 95, 116, -496, 44, 1331, -990, -2068, 2838, 1683, -4488, 0, 4488, -1683, -2838, 2068, 990, -1331, -44, 496, -116, -95, 46, 4, -6, 1).
%F A187240 a(n) = n^16/40320 - n^15/1080 + 7n^14/432 - 1153n^13/6480 + 53951n^12/38880 - 187277n^11/22680 + 106928053n^10/2721600 - 13957093n^9/90720 + 182160427n^8/362880 - 8821499n^7/6480 + 1176831457n^6/388800 - 490477369n^5/90720 + 8235592409n^4/1088640 - 726205757n^3/90720 + 1815275047n^2/302400 - 7953419n/2880 + 8491/16 + (-n^10/960 + 5n^9/144 - 307n^8/576 + 1793n^7/360 - 90571n^6/2880 + 201911n^5/1440 - 513865n^4/1152 + 477841n^3/480 - 4271471n^2/2880 + 1269721n/960 - 8491/16)*(-1)^n.
%F A187240 G.f.: -16x^5*(2520x^22 + 47160x^21 + 808884x^20 + 7825113x^19 + 54648810x^18 + 265795497x^17 + 965510650x^16 + 2638742416x^15 + 5598377728x^14 + 9280070520x^13 + 12189441400x^12 + 12689244954x^11 + 10499675700x^10 + 6853251794x^9 + 3501200340x^8 + 1373620536x^7 + 404231224x^6 + 85610168x^5 + 12313860x^4 + 1085765x^3 + 49362x^2 + 797x + 2)/((x-1)^17*(x+1)^11).
%F A187240 a(8) = A002465(8).
%t A187240 CoefficientList[Series[- 16 x^4 (2520 x^22 + 47160 x^21 + 808884 x^20 + 7825113 x^19 + 54648810 x^18 + 265795497 x^17 + 965510650 x^16 + 2638742416 x^15 + 5598377728 x^14 + 9280070520 x^13 + 12189441400 x^12 + 12689244954 x^11 + 10499675700 x^10 + 6853251794 x^9 + 3501200340 x^8 + 1373620536 x^7 + 404231224 x^6 + 85610168 x^5 + 12313860 x^4 + 1085765 x^3 + 49362 x^2 + 797 x + 2) / ((x - 1)^17 (x + 1)^11), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 02 2013 *)
%Y A187240 Cf. A172123, A172124, A172127, A172129, A176886, A187239.
%K A187240 nonn,easy
%O A187240 1,5
%A A187240 _Vaclav Kotesovec_, Mar 07 2011