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Search: id:A052468
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| A052468 |
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Numerators in the Taylor series for arcosh(x)-ln(2x). |
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+0
2
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| 1, 3, 5, 35, 63, 77, 429, 6435, 12155, 46189, 88179, 676039, 1300075, 5014575, 646323, 300540195, 583401555, 756261275, 4418157975, 6892326441, 22427411435, 263012370465, 514589420475, 2687300306925, 15801325804719
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A055786 is the preferred version of this sequence.
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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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a(n) / A052469(n) = A001147(n) / ( A000165(n) *2*n ). E.g. a(6) = 77 = 1*3*5*7*9*11 / gcd( 1*3*5*7*9*11, 2*4*6*8*10*12*12 )
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EXAMPLE
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I*Pi/2 - arccosh(x) = I*x + 1/6*I*x^3 + 3/40*I*x^5 + 5/112*I*x^7 + 35/1152*I*x^9 + 63/2816*I*x^11 + 231/13312*I*x^13 + 143/10240*I*x^15 + 6435/557056*I*x^17 + ...
0, 1, 0, 1/6, 0, 3/40, 0, 5/112, 0, 35/1152, 0, 63/2816, 0, 231/13312, 0, 143/10240, 0, 6435/557056, 0, 12155/1245184, 0, 46189/5505024, 0, ... = A052468/A052469
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CROSSREFS
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See A055786 for further information.
Essentially the same as A001790.
Sequence in context: A109173 A103010 A068111 this_sequence A055786 A001790 A057908
Adjacent sequences: A052465 A052466 A052467 this_sequence A052469 A052470 A052471
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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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