A012004 - OEIS

A012004

arcsinh(log(cos(x)))=-1/2!*x^2-2/4!*x^4-1/6!*x^6+148/8!*x^8-61/10!*x^10...

0, -1, -2, -1, 148, -61, -395702, -28299181, 93652648, 265509939239, 14066899733398, -8605652824527001, -2442549938212838852, 25891773268121861099, 210295085697229695516898

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OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

FORMULA

Lim sup n->infinity (|a(n)|/(2*n)!)^(1/n) = 1/(arccos(cos(1/2) - sin(1/2))^2 + arccosh(cos(1/2) + sin(1/2))^2) = 0.494130490883618452622838693... . - Vaclav Kotesovec, Mar 21 2016

MATHEMATICA

nmax = 20; Table[(CoefficientList[Series[ArcSinh[Log[Cos[x]]], {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[2*n+1]], {n, 0, nmax}] (* Vaclav Kotesovec, Mar 21 2016 *)

CROSSREFS

Sequence in context: A039923 A081708 A358858 * A101923 A010788 A258819

Adjacent sequences: A012001 A012002 A012003 * A012005 A012006 A012007

KEYWORD

sign

AUTHOR

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

EXTENSIONS

Prepended a(0)=0 from Vaclav Kotesovec, Mar 21 2016

STATUS

approved