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1, 12, 1680, 665280, 518918400, 670442572800, 1295295050649600, 3497296636753920000, 12576278705767096320000, 58102407620643984998400000, 335367096786357081410764800000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Expansion of cos(x^2).
Bisection of sequence A001813 - Gary W. Adamson, Jul 19 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
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FORMULA
| Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int((1/4)*exp(-1/4*sqrt(x))/(sqrt(Pi)*x^(3/4)), x=0..infinity), n=0, 1... - Karol A. Penson (penson(AT)lptl.jussieu.fr), Sep 19 2001
Contribution from Gary W. Adamson, Jul 19 2011: (Start)
a(n) = upper left term of M^(2n), where M = an infinite square production matrix as follows:
2, 2, 0, 0, 0, 0,...
4, 4, 4, 0, 0, 0,...
6, 6, 6, 6, 0, 0,...
8, 8, 8, 8, 8, 0,...
... (end)
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MATHEMATICA
| Cos[ x^2 ] (* [ x^(4n) ] *)
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PROG
| (MAGMA) [Factorial(4*n)/Factorial(2*n): n in [0..15]]; // Vincenzo Librandi, Jul 20 2011
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CROSSREFS
| Equals 4^n * A1002992(n).
Sequence in context: A015011 A034280 A146201 * A078928 A202968 A013717
Adjacent sequences: A009117 A009118 A009119 * A009121 A009122 A009123
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KEYWORD
| nonn,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended by Olivier Gerard, Mar 01, 1997
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