Search: id:A052468
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%I A052468
%S A052468 1,3,5,35,63,77,429,6435,12155,46189,88179,676039,1300075,5014575,
%T A052468 646323,300540195,583401555,756261275,4418157975,6892326441,
%U A052468 22427411435,263012370465,514589420475,2687300306925,15801325804719
%N A052468 Numerators in the Taylor series for arccosh(x)-ln(2x).
%C A052468 A055786 is the preferred version of this sequence.
%H A052468 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               InverseHyperbolicSecant.html">Link to a section of The World of Mathematics.</
               a>
%H A052468 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               InverseHyperbolicCosecant.html">Inverse Hyperbolic Cosecant</a>
%H A052468 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               InverseHyperbolicCosine.html">Inverse Hyperbolic Cosine</a>
%H A052468 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               InverseHyperbolicSine.html">Inverse Hyperbolic Sine</a>
%F A052468 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 )
%F A052468 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 
               2009: (Start)
%F A052468 a(n) = numer((2*n-1)!/(2^(2*n)*(n!)^2))
%F A052468 (End)
%e A052468 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 + ...
%e A052468 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
%Y A052468 See A055786 for further information.
%Y A052468 A52468(n)/A52469(n)=(1/(2*n))*A001790(n)/A046161(n) for n=>1.
%Y A052468 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 
               2009: (Start)
%Y A052468 Equals A162441(n+1)/(2n+1) for n=>1.
%Y A052468 (End)
%Y A052468 Sequence in context: A103010 A068111 A162444 this_sequence A055786 A001790 
               A057908
%Y A052468 Adjacent sequences: A052465 A052466 A052467 this_sequence A052469 A052470 
               A052471
%K A052468 nonn,easy,frac
%O A052468 1,2
%A A052468 Eric Weisstein (eric(AT)weisstein.com)
%E A052468 Updated May 22 2001 by Frank.Ellermann(AT)t-online.de
%E A052468 Cross-references edited by Johannes W. Meijer (meijgia(AT)hotmail.com), 
               Jul 05 2009

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