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 A180067 #24 Aug 05 2024 10:27:11
%S A180067 0,0,0,0,0,28,81095,42752576,2436444603,53633024900,666519047964,
%T A180067 5655962632720,36502953719310,191587564345044,854990702601025,
%U A180067 3346890268570368,11756179090049177,37692541754516628,111774885566128630,309788198526691600
%N A180067 Number of ways to place 9 nonattacking kings on an n X n toroidal board.
%H A180067 Vincenzo Librandi, <a href="/A180067/b180067.txt">Table of n, a(n) for n = 1..1000</a>
%H A180067 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>
%H A180067 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).
%F A180067 a(n) = 1/362880*n^2 * (n^16 -324*n^14 +46914*n^12 -3975048*n^10 +216203169*n^8 -7756575876*n^6 +179987135516*n^4 -2481599151792*n^2 +15651056776320), n>=10.
%F A180067 G.f.: -x^6*(56520x^22 - 1215064x^21 + 12642984x^20 - 82438064x^19 + 378510176x^18 - 1315100032x^17 + 3593010018x^16 - 7742517098x^15 + 12798616135x^14 - 15614945085x^13 + 14742135008x^12 - 17197088896x^11 + 33440162097x^10 - 55183782403x^9 + 50601858342x^8 - 7249042450x^7 - 32800069391x^6 + 23010354469x^5 + 14572795412x^4 + 1637985772x^3 + 41216559x^2 + 80563x + 28)/(x-1)^19.
%F A180067 General asymptotic formula for number of ways to place k nonattacking kings on an n X n toroidal board: n^2k/k! - 9/2*n^(2k-2)/(k-2)! + (243k+47)*n^(2k-4)/(24*(k-3)!) - (243k^2+141k+80)*n^(2k-6)/(16*(k-4)!) + (98415k^3+114210k^2+140645k+101762)*n^(2k-8)/(5760*(k-5)!)-...
%t A180067 CoefficientList[Series[- x^5 (56520 x^22 - 1215064 x^21 + 12642984 x^20 - 82438064 x^19 + 378510176 x^18 - 1315100032 x^17 + 3593010018 x^16 - 7742517098 x^15 + 12798616135 x^14 - 15614945085 x^13 + 14742135008 x^12 - 17197088896 x^11 + 33440162097 x^10 - 55183782403 x^9 + 50601858342 x^8 - 7249042450 x^7 - 32800069391 x^6 + 23010354469 x^5 + 14572795412 x^4 + 1637985772 x^3 + 41216559 x^2 + 80563 x + 28) / (x - 1)^19, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 01 2013 *)
%Y A180067 Cf. A179403, A179404, A179424, A179425, A179426, A179427, A179428.
%K A180067 nonn,easy
%O A180067 1,6
%A A180067 _Vaclav Kotesovec_, Jan 15 2011