A012942 arcsinh(tan(x)+sin(x))=2*x-7/3!*x^3+265/5!*x^5-25057/7!*x^7...

2, -7, 265, -25057, 4755625, -1487826157, 695606193685, -454203430112257, 394845201696352945, -440870517608275534357, 614891740513394365279405, -1047641908006405960227528457, 2141116578378965145859645589065

Offset

0,1

Links

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

Formula

a(n) ~ c * (-1)^n * (2*n)! / (sqrt(n) * r^(2*n)), where r = log(1/sqrt(2) + sqrt(sqrt(2)-1/2)) = 0.50877468529164966260597020663038274... is the root of the equation sinh(r) + tanh(r) = 1, c = 1.093803299898438252433636778285467... . - Vaclav Kotesovec, Feb 04 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[ArcSinh[Sin[x] + Tan[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: A294827 A295610 A329967 * A208018 A013058 A013097

Adjacent sequences: A012939 A012940 A012941 * A012943 A012944 A012945

Keyword

sign

Author

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

Status

approved