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1, 6, 120, 5040, 362880, 39916800, 6227020800, 1307674368000, 355687428096000, 121645100408832000, 51090942171709440000, 25852016738884976640000, 15511210043330985984000000, 10888869450418352160768000000, 8841761993739701954543616000000, 8222838654177922817725562880000000
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OFFSET
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0,2
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COMMENTS
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Denominators in the expansion of sin(x):
sin(x) = x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - ...
Denominators in the expansion of sinc x = sin(x)/x:
sinc x = sin(x)/x = 1 - x^2/3! + x^4/5! - x^6/7! + x^8/9! - ... - Daniel Forgues, Oct 20 2011
a(n) = A014481(n) * A001147(n). - _Reinhard Zumkeller, Dec 03 2011
This sequence is the denominator of sinh(x) = (e^x-e^(-x))/2 = x + x^3/3! + x^5/5! + x^7/7! + .... - Mohammad K. Azarian, Jan 19 2012
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REFERENCES
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W. Dunham, Touring the calculus gallery, Amer. Math. Monthly, 112 (2005), 1-19.
H. B. Dwight, Tables of Integrals and Other Mathematical Data, Macmillan, NY, 1968, p. 88.
I. Newton, De analysi, 1669; reprinted in D. Whiteside, ed., The Mathematical Works of Isaac Newton, vol. 1, Johnson Reprint Co., 1964; see p. 20.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric Weisstein's World of Mathematics, Hyperbolic Sine
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PROG
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sage: [stirling_number1(2*i, 1) for i in xrange(1, 22)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2008
(PARI) a(n)=(n+n+1)! \\ Charles R Greathouse IV, Oct 20 2011
(MAGMA) [Factorial(2*n+1): n in [0..20]]; // Vincenzo Librandi, Oct 21 2011
(Haskell)
a009445 n = product [1..2*n+1] -- Reinhard Zumkeller, Dec 03 2011
(Sage)
T = taylor(sin(x^2), x, 0, 70)
[(-1)^n/T.coeff(x, 4*n+2) for n in (0..15)] # Peter Luschny, Dec 14 2012
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CROSSREFS
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Cf. A010050, A000142.
Sequence in context: A057003 A096718 A096720 * A094273 A094278 A093910
Adjacent sequences: A009442 A009443 A009444 * A009446 A009447 A009448
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KEYWORD
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nonn,easy
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AUTHOR
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R. H. Hardin, Joe Keane (jgk(AT)jgk.org)
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STATUS
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approved
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