A179064 Number of non-attacking placements of 9 rooks on an n X n board.
0, 0, 0, 0, 0, 0, 0, 0, 362880, 36288000, 1097712000, 17563392000, 185513328000, 1454424491520, 9090153072000, 47491411968000, 214453407168000, 857813628672000, 3096707199505920, 10237048593408000, 31350961317312000
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 (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).
Programs
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PARI
a(n) = 9! * binomial(n, 9)^2 \\ Andrew Howroyd, Feb 13 2018
Formula
a(n) = 9!*binomial(n,9)^2.
G.f.: -362880*x^9*(x +1)*(x^8 +80*x^7 +1216*x^6 +5840*x^5 +10036*x^4 +5840*x^3 +1216*x^2 +80*x +1) / (x -1)^19. - Colin Barker, Jan 08 2013