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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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5
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1, 4, 144, 14400, 2822400, 914457600, 442597478400, 299195895398400, 269276305858560000, 311283409572495360000, 449493243422683299840000, 792906081397613340917760000, 1677789268237349829381980160000, 4194473170593374573454950400000000, 12231083765450280256194635366400000000
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OFFSET
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0,2
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COMMENTS
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a(n) appears as coefficient of x^(2*n)/n! in the expansion of 1/sqrt(1-4*x^2). - Wolfdieter Lang, Oct 06 2008
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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). (Q_{8n+1}, Eq. (22))
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FORMULA
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Sum_{n>=0} 1/a(n) = 1 + L_0(1/2)*Pi/4, where L is the modified Struve function.
Sum_{n>=0} (-1)^n/a(n) = 1 - H_0(1/2)*Pi/4, where H is the Struve function. (End)
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EXAMPLE
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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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MATHEMATICA
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Array[((2#)!/#!)^2 &, 15, 0] (* Amiram Eldar, Dec 16 2018 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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