%I #19 Feb 13 2018 18:13:06
%S 0,0,0,0,0,0,5040,322560,6531840,72576000,548856000,3161410560,
%T 14841066240,59364264960,208702494000,659602944000,1906252508160,
%U 5104345559040,12796310741760,30287126016000,68146033536000
%N Number of non-attacking placements of 7 rooks on an n X n board.
%H Andrew Howroyd, <a href="/A179062/b179062.txt">Table of n, a(n) for n = 1..200</a>
%H 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 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F a(n) = 7!*binomial(n,7)^2.
%F G.f.: -5040*x^7*(x+1)*(x^6+48*x^5+393*x^4+832*x^3+393*x^2+48*x+1) / (x-1)^15. - _Colin Barker_, Jan 08 2013
%t 7! Binomial[Range[30],7]^2 (* or *) LinearRecurrence[{15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1},{0,0,0,0,0,0,5040,322560,6531840,72576000,548856000,3161410560,14841066240,59364264960,208702494000},30] (* _Harvey P. Dale_, May 25 2017 *)
%o (PARI) a(n) = 7! * binomial(n, 7)^2 \\ _Andrew Howroyd_, Feb 13 2018
%Y Column k=7 of A144084.
%Y Cf. A179061 (6 rooks), A179063 (8 rooks).
%K easy,nonn
%O 1,7
%A _Thomas Zaslavsky_, Jun 27 2010