A012641 - OEIS

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A012641

tanh(arcsinh(x)*cos(x))=x-6/3!*x^3+120/5!*x^5-6216/7!*x^7...

1, -6, 120, -6216, 548544, -74860544, 14571230336, -3827313412352, 1304171528695808, -559299942314340352, 294737591597024591872, -187195194238509459439616, 141014910901971840963870720

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OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..218

FORMULA

a(n) ~ c * (-1)^n * (2*n)! * n / r^(2*n), where r = 0.8922083063567712426146182695087047187586345275404... is the root of the equation arcsin(r)*cosh(r) = Pi/2, c = 1.175488110258... . - Vaclav Kotesovec, Feb 04 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[Tanh[ArcSinh[x]*Cos[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 04 2015 *)

CROSSREFS

Sequence in context: A002370 A012846 A331640 * A012795 A054479 A012475

Adjacent sequences: A012638 A012639 A012640 * A012642 A012643 A012644

KEYWORD

sign

AUTHOR

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

STATUS

approved