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Search: id:A122747
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| A122747 |
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Bishops on an n X n board (see Robinson paper for details). |
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+0
2
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| 1, 4, 144, 14400, 2822400, 914457600, 442597478400, 299195895398400, 269276305858560000, 311283409572495360000, 449493243422683299840000, 792906081397613340917760000, 1677789268237349829381980160000, 4194473170593374573454950400000000, 12231083765450280256194635366400000000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) appears as coefficient of x^(2*n)/n! in the expansion of 1/sqrt(1-4*x^2). [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 06 2008]
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REFERENCES
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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). (Q_{8n+1}, Eq. (22))
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EXAMPLE
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a(n)= ((2*n)!/n!)^2 = A001813(n)^2. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 06 2008]
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MAPLE
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Q:=proc(n) local m; if n mod 8 <> 1 then RETURN(0); fi; m:=(n-1)/8; ((2*m)!)^2/(m!)^2; end;
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CROSSREFS
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Adjacent sequences: A122744 A122745 A122746 this_sequence A122748 A122749 A122750
Sequence in context: A036511 A060870 A084703 this_sequence A069135 A138176 A055209
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Sep 25 2006
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