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A067624
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sqrt((1+cos(x))/2) = sum(n>=0, (-1)^n * x^(2*n) /a(n) ).
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3
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1, 8, 384, 46080, 10321920, 3715891200, 1961990553600, 1428329123020800, 1371195958099968000, 1678343852714360832000, 2551082656125828464640000, 4714400748520531002654720000, 10409396852733332453861621760000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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 (jmaxwellcampbell(AT)gmail.com), June 4 2011]
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FORMULA
| a(n)=A000165(2*n) where A000165(k) are the double factorial numbers 2^k*k!=(2k)!! [Corrected by Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 05 2009]
a(n) = (4*n)!! = 2^(2*n)*(2*n)! [Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009]
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MAPLE
| for n from 0 to 30 by 2 do printf(`%d, `, 2^(n)*(n)!) od:
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MATHEMATICA
| 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}] (* From John M. Campbell (jmaxwellcampbell(AT)gmail.com), June 4 2011 *)
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CROSSREFS
| Cf. A000165.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)
Appears in A162445, A061549 and A120738.
(End)
Sequence in context: A151932 A096205 A162445 * A096204 A153836 A151941
Adjacent sequences: A067621 A067622 A067623 * A067625 A067626 A067627
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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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