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A013052
arctanh(sinh(x)+tan(x))=2*x+19/3!*x^3+1025/5!*x^5+138129/7!*x^7...
0
2, 19, 1025, 138129, 34734545, 14037224089, 8320152726665, 6799527662204049, 7327672308214372385, 10068470883926665540009, 17180000319605942481431705, 35640287243130630709541583969
OFFSET
0,1
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
KEYWORD
nonn
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
STATUS
approved