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A067624
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a(n) = 2^(2*n)*(2*n)!.
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7
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1, 8, 384, 46080, 10321920, 3715891200, 1961990553600, 1428329123020800, 1371195958099968000, 1678343852714360832000, 2551082656125828464640000, 4714400748520531002654720000, 10409396852733332453861621760000
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OFFSET
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0,2
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COMMENTS
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For n >= 1, a(n) equals the absolute value of the determinant of the 4n X 4n matrix with i's along the superdiagonal (where i is the imaginary unit), and 2, 3, 4, ... 4*n along the subdiagonal, and 0's everywhere else. (See Mathematica code below.) - John M. Campbell, Jun 04 2011
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LINKS
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FORMULA
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sqrt((1+cos(x))/2) = Sum_{n>=0} (-1)^n * x^(2*n) / a(n).
Sum_{n>=0} 1/a(n) = cosh(1/2).
Sum_{n>=0} (-1)^n/a(n) = cos(1/2). (End)
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MAPLE
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for n from 0 to 30 by 2 do printf(`%d, `, 2^(n)*(n)!) od: # James A. Sellers, Feb 11 2002
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MATHEMATICA
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Table[Abs[Det[Array[KroneckerDelta[#1 + 1, #2]*I &, {4*n, 4*n}] + Array[KroneckerDelta[#1 - 1, #2]*#1 &, {4*n, 4*n}]]], {n, 1, 20}] (* John M. Campbell, Jun 04 2011 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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