A012712 E.g.f.: tan(arctanh(x)*exp(x)).

0, 1, 2, 7, 36, 285, 2470, 25891, 304584, 4116473, 61307338, 1011045759, 18130445036, 353222430613, 7401849057902, 166375042595867, 3987022624401808, 101564702642995953, 2738893925584229778, 77978462505905882103, 2336771614133464558516, 73533230212519134743821

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) ~ n! * (sin(exp(r) * arctanh(r)))^2 / (exp(r) * (arctanh(r) + 1/(1-r^2)) * r^(n+1)), where r = 0.6673395955783244309800035195157735575759307410912847... is the root of the equation arctanh(r)*exp(r) = Pi/2. - Vaclav Kotesovec, Feb 05 2015

Example

tan(arctanh(x)*exp(x)) = x+2/2!*x^2+7/3!*x^3+36/4!*x^4+285/5!*x^5...

Mathematica

With[{nn=20}, CoefficientList[Series[Tan[ArcTanh[x]Exp[x]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Mar 05 2013 *)

Prog

(PARI) x='x+O('x^66); concat([0], Vec(serlaplace(tan(atanh(x)*exp(x))))) \\ Joerg Arndt, Mar 05 2013

Crossrefs

Sequence in context: A009704 A141308 A185161 * A012363 A012717 A072236

Adjacent sequences: A012709 A012710 A012711 * A012713 A012714 A012715

Keyword

nonn

Author

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

Extensions

a(0) = 0 added by Harvey P. Dale, Mar 05 2013

Offset corrected by Vaclav Kotesovec, Feb 05 2015

Status

approved