1,2

A055786 is the preferred version of this sequence.

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

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)

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

See A055786 for further information.

A52468(n)/A52469(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: A103010 A068111 A162444 this_sequence A055786 A001790 A057908

Adjacent sequences: A052465 A052466 A052467 this_sequence A052469 A052470 A052471

nonn,easy,frac

Eric Weisstein (eric(AT)weisstein.com)

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