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Search: id:A009001
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| A009001 |
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Expansion of (1+x)*cos(x). |
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+0
5
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| 1, 1, -1, -3, 1, 5, -1, -7, 1, 9, -1, -11, 1, 13, -1, -15, 1, 17, -1, -19, 1, 21, -1, -23, 1, 25, -1, -27, 1, 29, -1, -31, 1, 33, -1, -35, 1, 37, -1, -39, 1, 41, -1, -43, 1, 45, -1, -47, 1, 49, -1, -51, 1, 53, -1, -55, 1, 57, -1, -59, 1, 61, -1, -63, 1, 65, -1, -67, 1, 69, -1, -71, 1, 73, -1, -75, 1, 77, -1, -79, 1, 81, -1, -83, 1, 85
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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If signs are ignored, continued fraction for tan(1) (cf. A093178).
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
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FORMULA
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(-1)^(n/2) if n even, n*(-1)^((n-1)/2) if n odd.
a(n) =(n^n mod (n+1))*(-1)^[n/2] for n>0 =(-1)^n*(a(n-2)-a(n-1))-a(n-3) for n>2. - Henry Bottomley (se16(AT)btinternet.com), Oct 19 2001
G.f.: (1+x+x^2-x^3)/(1+x^2)^2. E.g.f: (1+x)*cos(x).
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EXAMPLE
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tan(1) = 1.557407724654902230... = 1 + 1/(1 + 1/(1 + 1/(3 + 1/(1 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 15 2009]
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MATHEMATICA
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Cos[ x ]*(1+x)
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PROGRAM
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(PARI) {a(n)=(-1)^(n\2)*if(n%2, n, 1)} /* Michael Somos Oct 16 2006 */
(PARI) { allocatemem(932245000); default(realprecision, 79000); x=contfrac(tan(1)); for (n=0, 20000, write("b009001.txt", n, " ", (-1)^(n\2)*x[n+1])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 15 2009]
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CROSSREFS
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Cf. A009531.
Cf. A049471 Decimal expansion of tan(1). [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 15 2009]
Sequence in context: A090585 A147661 A155457 this_sequence A093178 A093411 A147088
Adjacent sequences: A008998 A008999 A009000 this_sequence A009002 A009003 A009004
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KEYWORD
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sign,easy,nice
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AUTHOR
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R. H. Hardin (rhhardin(AT)att.net), N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe, David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Formula corrected Mar 15 1997 by Olivier Gerard
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