A194788 - OEIS

%I #14 Jan 13 2018 22:07:53

%S 0,0,0,0,242,51504,2484382,44601420,450193818,3112919712,16471667554,

%T 71393226972,265069706646,869583076752,2577681275622,7020477731884,

%U 17794428237522,42397762374912,95726217156906,206149749502012,425731784898894,846919172059632

%N Number of ways to place 7 nonattacking kings on an n X n board.

%H 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>

%F a(n) = (n^14 - 189n^12 + 252n^11 + 15211n^10 - 38640n^9 - 649215n^8 + 2408700n^7 + 14771764n^6 - 75856200n^5 - 144099396n^4 + 1198867488n^3 - 255900576n^2 - 7543005120n + 10617929280)/5040, n>=6. - _Andrew Woods_, Sep 02 2011

%F G.f.: 2*x^5*(1930*x^15 - 20052*x^14 + 87663*x^13 - 265681*x^12 + 816798*x^11 - 2117376*x^10 + 2865281*x^9 + 557737*x^8 - 6577818*x^7 + 3848604*x^6 + 8828017*x^5 - 9464319*x^4 - 6316750*x^3 - 868616*x^2 - 23937*x - 121)/ (x-1)^15. - _Vaclav Kotesovec_, Nov 06 2011

%Y Cf. A061995, A061996, A061997, A061998, A172158.

%K nonn

%O 1,5

%A _Andrew Woods_, Sep 02 2011