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A067626
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sqrt((1-cos(x))/2) = sum(n>=0, (-1)^n * x^(2*n+1) / a(n) ).
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0
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2, 48, 3840, 645120, 185794560, 81749606400, 51011754393600, 42849873690624000, 46620662575398912000, 63777066403145711616000, 107145471557284795514880000, 216862434431944426122117120000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n) equals the absolute value of the imaginary part of the determinant of the (4n+2) X (4n+2) matrix with i's along the superdiagonal (where i is the imaginary unit) and 2, 3, 4, ..., 4n+2 along the subdiagonal, and 0's everywhere else (see Mathematica code below). [From John M. Campbell (jmaxwellcampbell(AT)gmail.com), June 4, 2011]
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LINKS
| Eric Weisstein's World of Mathematics, Riemann-Siegel Functions
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FORMULA
| a(n)=A000165(2n+2) where A000165(k) are the double factorial numbers 2^k*k!=(2k)!!
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MAPLE
| for n from 0 to 30 by 2 do printf(`%d, `, 2^(n+1)*(n+1)!) od:
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MATHEMATICA
| Table[Abs[Im[Det[Array[KroneckerDelta[#1 + 1, #2]*I &, {4*n + 2, 4*n + 2}] + Array[KroneckerDelta[#1 - 1, #2]*#1 &, {4*n + 2, 4*n + 2}]]]], {n, 0, 20}] (* From John M. Campbell (jmaxwellcampbell(AT)gmail.com), June 4, 2011 *)
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CROSSREFS
| Cf. A000165.
Sequence in context: A114714 A186416 A087085 * A053071 A002820 A196448
Adjacent sequences: A067623 A067624 A067625 * A067627 A067628 A067629
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2002
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EXTENSIONS
| More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Feb 11, 2002
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