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A000899
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Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).
(Formerly M4645 N1987)
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23
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0, 0, 0, 1, 9, 70, 571, 4820, 44676, 450824, 4980274, 59834748, 778230060, 10896609768, 163456629604, 2615335902176, 44460874280032, 800296440705472, 15205636325496568, 304112744618157872, 6386367741011250672
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OFFSET
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1,5
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REFERENCES
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L. C. Larson, The number of essentially different nonattacking rook arrangements, J. Recreat. Math., 7 (No. 3, 1974), circa pages 180-181.
R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (Annotated scanned copy)
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FORMULA
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For asymptotics see the Robinson paper.
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MAPLE
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MATHEMATICA
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a[n_] := ((n+1)! - (2*Floor[(n+1)/2])!! - 2*Sum[Binomial[n+1, 2*k]*(2*k-1)!!, {k, 0, (n+1)/2}] + 2*Sum[2^k*BellB[k]*StirlingS1[Floor[(n+1)/2], k], {k, 0, Floor[(n+1)/2]}])/8; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Dec 23 2013, from explicit formulas *)
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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