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 A172158 #27 Apr 23 2022 18:36:54
%S A172158 0,0,0,0,978,62266,1220298,12033330,77784658,377818258,1492665418,
%T A172158 5042436754,15062292834,40736208186,101489568538,235984235970,
%U A172158 517314078210,1077720399538,2147500025914,4114538426818,7613150953522,13653752767866,23808409699242
%N A172158 Number of ways to place 6 nonattacking kings on an n X n board.
%H A172158 Vincenzo Librandi, <a href="/A172158/b172158.txt">Table of n, a(n) for n = 1..1000</a>
%H A172158 Vaclav 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>
%H A172158 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78, -13,1).
%F A172158 a(n) = (n^12 - 135*n^10 + 180*n^9 + 7465*n^8 - 18840*n^7 - 202665*n^6 + 751860*n^5 + 2442334*n^4 - 13441200*n^3 - 3643800*n^2 + 89860320*n - 108217440)/720, n>=5. For any fixed value of k > 1, a(n) = n^(2*k)/k! - 9*n^(2*k-2)/2/(k-2)! + 6*n^(2*k-3)/(k-2)! ... - _Vaclav Kotesovec_, Jan 27 2010
%F A172158 G.f.: 2*x^5 * (489 + 24776*x + 243562*x^2 + 373248*x^3 - 287097*x^4 - 263140*x^5 + 376992*x^6 - 162056*x^7 + 36103*x^8 - 20892*x^9 + 14622*x^10 - 4432*x^11 + 465*x^12)/(1-x)^13. - _Vaclav Kotesovec_, Mar 24 2010
%t A172158 CoefficientList[Series[2*x^4*(489 +24776*x +243562*x^2 +373248*x^3 -287097*x^4 -263140*x^5 +376992*x^6 -162056*x^7 +36103*x^8 -20892*x^9 +14622*x^10 -4432*x^11 +465*x^12)/(1-x)^13, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 27 2013 *)
%o A172158 (SageMath) [0,0,0,0]+[(n^12 -135*n^10 +180*n^9 +7465*n^8 -18840*n^7 -202665*n^6 + 751860*n^5 +2442334*n^4 -13441200*n^3 -3643800*n^2 +89860320*n -108217440)/720 for n in (5..40)] # _G. C. Greubel_, Apr 21 2022
%Y A172158 Cf. A061995, A061996, A061997, A061998.
%K A172158 nonn,easy
%O A172158 1,5
%A A172158 _Vaclav Kotesovec_, Jan 27 2010
%E A172158 More terms from _Vincenzo Librandi_, May 27 2013