A012755 - OEIS

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A012755

tan(arctanh(x)*tanh(x))=2/2!*x^2+400/6!*x^6+2688/8!*x^8...

0, 2, 0, 400, 2688, 1631488, 60938240, 35243972608, 3826154307584, 2477263324839936, 571708399442198528, 435722170330996801536, 177081722613295659089920, 162107313371111569999527936

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) ~ (2*n)! * sinh(2*r) / ((Pi/2 + (sinh(r))^2/(1-r^2)) * r^(2*n+1)), where r = 0.970313828446324195188532490988552661547225320103102781254845... is the root of the equation arctanh(r)*tanh(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[Tan[ArcTanh[x]*Tanh[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 06 2015 *)

CROSSREFS

Sequence in context: A012449 A012446 A324687 * A012452 A339269 A013417

Adjacent sequences: A012752 A012753 A012754 * A012756 A012757 A012758

KEYWORD

nonn

AUTHOR

Patrick Demichel (patrick.demichel(AT)hp.com)

EXTENSIONS

a(0)=0 prepended by Vaclav Kotesovec, Feb 06 2015

STATUS

approved