A013052 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A013052

arctanh(sinh(x)+tan(x))=2*x+19/3!*x^3+1025/5!*x^5+138129/7!*x^7...

2, 19, 1025, 138129, 34734545, 14037224089, 8320152726665, 6799527662204049, 7327672308214372385, 10068470883926665540009, 17180000319605942481431705, 35640287243130630709541583969

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..11.

FORMULA

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.47191303538345047716706116017105574144998... is the root of the equation sinh(r)+tan(r) = 1. - Vaclav Kotesovec, Feb 05 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[ArcTanh[Sinh[x] + Tan[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 05 2015 *)

With[{nn=30}, Take[CoefficientList[Series[ArcTanh[Sinh[x]+Tan[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Jul 14 2024 *)

CROSSREFS

Sequence in context: A015191 A165937 A128345 * A012956 A012976 A013107

Adjacent sequences: A013049 A013050 A013051 * A013053 A013054 A013055

KEYWORD

nonn

AUTHOR

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

STATUS

approved