A012031 arcsinh(sin(sinh(x)))=x-1/3!*x^3+1/5!*x^5-113/7!*x^7+4033/9!*x^9...

1, -1, 1, -113, 4033, -307297, 32041153, -4722808145, 919792817281, -229762987386049, 71595055755086977, -27226195625057526833, 12411835138553868048961, -6681718218812850626513185

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..226

Formula

a(n) ~ (2*n)! * (-1)^n * c / (sqrt(n) * (arcsin(log(1+sqrt(2))))^(2*n)), where c = 0.444000919811565867306663265... . - Vaclav Kotesovec, Feb 03 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[ArcSinh[Sin[Sinh[x]]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 03 2015 *)

Crossrefs

Sequence in context: A008362 A262074 A200854 * A283781 A350054 A250052

Adjacent sequences: A012028 A012029 A012030 * A012032 A012033 A012034

Keyword

sign

Author

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

Status

approved