A012741 tan(arctanh(x)*cos(x))=x+1/3!*x^3+5/5!*x^5+509/7!*x^7+44393/9!*x^9...

1, 1, 5, 509, 44393, 4436441, 630529965, 126873147413, 33552906028625, 11170776120292657, 4582643056340650197, 2275243986686803354029, 1344475182597566546716345, 932197702028175163027746313

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..223

Vaclav Kotesovec, Graph - abs(e.g.f.) in the complex plane

Formula

a(n) ~ 4 * (2*n+1)! / ((2*(cos(r)/(1-r^2)) - Pi*tan(r)) * r^(2*n+2)), where r = 0.993706174320375134478924859424390533447067228384145975655366... is the root of the equation arctanh(r)*cos(r) = Pi/2. - Vaclav Kotesovec, Feb 07 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcTanh[x]*Cos[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 06 2015 *)

Crossrefs

Sequence in context: A128682 A228093 A068234 * A317821 A318428 A318096

Adjacent sequences: A012738 A012739 A012740 * A012742 A012743 A012744

Keyword

nonn

Author

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

Status

approved