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A052468
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Numerators in the Taylor series for arccosh(x)-ln(2x).
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3
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A055786 is the preferred version of this sequence.
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LINKS
| 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
| 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 )
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)
a(n) = numer((2*n-1)!/(2^(2*n)*(n!)^2))
(End)
Let z(n)=2*(2*n+1)!*4^(-n-1)/((n+1)!)^2, then a(n)=numer(z(n)), A162442(n)=denom(z(n)), and z(n)=1/(n+1)-sum((-1)^k*binomial(n,k)*z(k),k=0..n) [From Groux Roland, Jan 04 2011]
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EXAMPLE
| 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
| See A055786 for further information.
A052468(n)/A052469(n)=(1/(2*n))*A001790(n)/A046161(n) for n=>1.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)
Equals A162441(n+1)/(2n+1) for n=>1.
(End)
Sequence in context: A187993 A068111 A162444 * A055786 A001790 A173092
Adjacent sequences: A052465 A052466 A052467 * A052469 A052470 A052471
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KEYWORD
| nonn,easy,frac,changed
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| Updated May 22 2001 by Frank.Ellermann(AT)t-online.de
Cross-references edited by Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 05 2009
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