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Search: id:A052469
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| A052469 |
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Denominators in the Taylor series for arccosh(x)-ln(2x). |
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+0
5
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| 4, 32, 96, 1024, 2560, 4096, 28672, 524288, 1179648, 5242880, 11534336, 100663296, 218103808, 939524096, 134217728, 68719476736, 146028888064, 206158430208, 1305670057984, 2199023255552, 7696581394432
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Bronstein-Semendjajew, sprawotchnik po matematikje, 6th russian ed. 1956, ch. 4.2.6
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Inverse Hyperbolic Cosecant
Eric Weisstein's World of Mathematics, Inverse Hyperbolic Cosine
Eric Weisstein's World of Mathematics, Inverse Hyperbolic Sine
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FORMULA
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Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)
a(n) = denom((2*n-1)!/( 2^(2*n)* (n!)^2))
(End)
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EXAMPLE
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arccosh(x) = ln(2x) - 1/(4*x^2) - 3/(32*x^4) - 5/(96*x^6) - .. for x>1
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CROSSREFS
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Cf. A002595.
A052468(n) / a(n) = A001147(n) / ( A000165(n) *2*n )
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)
Equals 2*A162442(n+1) for n =>1.
A52468(n)/A52469(n) = (1/(2*n))*A001790(n)/A046161(n) for n=>1.
(End)
Sequence in context: A012036 A153794 A108914 this_sequence A033430 A088658 A088802
Adjacent sequences: A052466 A052467 A052468 this_sequence A052470 A052471 A052472
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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Updated May 22 2001 by Frank.Ellermann(AT)t-online.de
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