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Search: id:A010050
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| 1, 2, 24, 720, 40320, 3628800, 479001600, 87178291200, 20922789888000, 6402373705728000, 2432902008176640000, 1124000727777607680000, 620448401733239439360000, 403291461126605635584000000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Denominators in the expansion of cos(x): cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! - ...
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REFERENCES
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W. Dunham, Touring the calculus gallery, Amer. Math. Monthly, 112 (2005), 1-19.
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.
H. B. Dwight, Tables of Integrals and Other Mathematical Data, Macmillan, NY, 1968, p. 88.
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LINKS
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Eric Weisstein's World of Mathematics, Hyperbolic Cosine
Index entries for related partition-counting sequences
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FORMULA
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E.g.f. for sequence with alt. signs: arctan(x).
E.g.f. : 1/(1-x^2) (with interpolated zeros). - Paul Barry (pbarry(AT)wit.ie), Sep 14 2004
a(n+1) = a(n)*(2n+1)*(2n+2) = a(n)*A002939(n-1). - Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 29 2005
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MATHEMATICA
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s=1; lst={s}; Do[s+=(s*=n)*n; AppendTo[lst, s], {n, 1, 5!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 15 2008]
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CROSSREFS
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Cf. A000142, A000165, A009445.
Bisection of A005359, |A012251|, A012254, A070734.
Adjacent sequences: A010047 A010048 A010049 this_sequence A010051 A010052 A010053
Sequence in context: A046977 A119699 A093459 this_sequence A012161 A009724 A009396
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KEYWORD
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nonn,easy
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AUTHOR
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Joe Keane (jgk(AT)jgk.org)
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