A179062 Number of non-attacking placements of 7 rooks on an n X n board.
0, 0, 0, 0, 0, 0, 5040, 322560, 6531840, 72576000, 548856000, 3161410560, 14841066240, 59364264960, 208702494000, 659602944000, 1906252508160, 5104345559040, 12796310741760, 30287126016000, 68146033536000
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853, a12016
- Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
Programs
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Mathematica
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 *) -
PARI
a(n) = 7! * binomial(n, 7)^2 \\ Andrew Howroyd, Feb 13 2018
Formula
a(n) = 7!*binomial(n,7)^2.
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