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 A178140 #17 Aug 21 2024 10:53:39
%S A178140 0,0,0,0,0,0,5040,589824,6531840,98304000,548856000,3822059520,
%T A178140 14841066240,67711795200,208702494000,726855843840,1906252508160,
%U A178140 5500708061184,12796310741760,32142458880000,68146033536000
%N A178140 Number of ways to place 7 nonattacking bishops on an n X n toroidal board.
%H A178140 Vincenzo Librandi, <a href="/A178140/b178140.txt">Table of n, a(n) for n = 1..1000</a>
%H A178140 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013
%H A178140 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (2, 12, -26, -65, 156, 208, -572, -429, 1430, 572, -2574, -429, 3432, 0, -3432, 429, 2574, -572, -1430, 429, 572, -208, -156, 65, 26, -12, -2, 1).
%F A178140 Explicit formula (Vaclav Kotesovec, May 21 2010): (1/10080)*(n-6)^2*(n-4)^2*(n-2)^2*(n^2) * (2*n^6 -36*n^5 +275*n^4 -1224*n^3 +3887*n^2 -9570*n +14625 +(21*n^4 -336*n^3 +2289*n^2 -8190*n +14175)*(-1)^n).
%F A178140 G.f.: -48*x^7 * (105*x^20 +32558*x^19 +69284*x^18 +2532234*x^17 +4270573*x^16 +43976860*x^15 +59687712*x^14 +262529316*x^13 +264238506*x^12 +619225992*x^11 +438942840*x^10 +606753672*x^9 +289183146*x^8 +243462436*x^7 +72876832*x^6 +36501660*x^5 +6031853*x^4 +1631114*x^3 +110244*x^2 +12078*x +105) / ((x-1)^15*(x+1)^13).
%t A178140 CoefficientList[Series[- 48 x^6 (105 x^20 + 32558 x^19 + 69284 x^18 + 2532234 x^17 + 4270573 x^16 + 43976860 x^15 + 59687712 x^14 + 262529316 x^13 + 264238506 x^12 + 619225992 x^11 + 438942840 x^10 + 606753672 x^9 + 289183146 x^8 + 243462436 x^7 + 72876832 x^6 + 36501660 x^5 + 6031853 x^4 + 1631114 x^3 + 110244 x^2 + 12078 x + 105) / ((x - 1)^15 (x + 1)^13), {x, 0, 50}], x] (* _Vincenzo Librandi_, May 31 2013 *)
%Y A178140 Cf. A177755, A177756, A177757, A177758, A177759, A176886.
%K A178140 nonn,easy
%O A178140 1,7
%A A178140 _Vaclav Kotesovec_, May 21 2010