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A179064
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Number of non-attacking placements of 9 rooks on an n X n board.
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4
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0, 0, 0, 0, 0, 0, 0, 0, 362880, 36288000, 1097712000, 17563392000, 185513328000, 1454424491520, 9090153072000, 47491411968000, 214453407168000, 857813628672000, 3096707199505920, 10237048593408000, 31350961317312000
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OFFSET
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1,9
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LINKS
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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
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FORMULA
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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
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PROG
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(PARI) a(n) = 9! * binomial(n, 9)^2 \\ Andrew Howroyd, Feb 13 2018
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CROSSREFS
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Column k=9 of A144084.
Cf. A179063 (8 rooks), A179065 (10 rooks).
Sequence in context: A254082 A228912 A213871 * A246197 A246617 A246220
Adjacent sequences: A179061 A179062 A179063 * A179065 A179066 A179067
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KEYWORD
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easy,nonn
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AUTHOR
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Thomas Zaslavsky, Jun 28 2010
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STATUS
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approved
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