A012738 exp(arctanh(x)*cos(x)) = 1+x+1/2!*x^2-3/4!*x^4+45/6!*x^6+504/7!*x^7...

1, 1, 1, 0, -3, 0, 45, 504, 2457, 24384, 161625, 2375296, 20549397, 338479232, 3457938757, 64501554688, 772773915313, 16130341302272, 221864504883633, 5112670099460096, 79479234590193325, 2003580047549120512

Offset

0,5

Links

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

Formula

a(n) ~ (n-1)! * (2*n)^(cos(1)/2) / GAMMA(cos(1)/2) * (1 - (-1)^n*cos(1)*sin(Pi*cos(1)/2)*(GAMMA(cos(1)/2))^2/(2*Pi*(2*n)^cos(1))). - Vaclav Kotesovec, Oct 24 2013

Mathematica

CoefficientList[Series[Exp[ArcTanh[x]*Cos[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 24 2013 *)

Crossrefs

Sequence in context: A177698 A377240 A009786 * A193410 A271762 A264882

Adjacent sequences: A012735 A012736 A012737 * A012739 A012740 A012741

Keyword

sign

Author

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

Status

approved