A012785 tan(sec(x)*arcsin(x))=x+6/3!*x^3+140/5!*x^5+7616/7!*x^7+731856/9!*x^9...

1, 6, 140, 7616, 731856, 108552224, 22943169600, 6543956234752, 2420812240335104, 1126850609820597760, 644442125440553221120, 444134934522130204704768, 363006744066808568769433600

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

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

Formula

a(n) ~ 4 * cos(r) * (2*n+1)! / ((2/sqrt(1-r^2) + Pi*sin(r)) * r^(2*n+2)), where r = 0.85667809568102855617374657046258339292906641041135819687798... is the root of the equation sec(r)*arcsin(r) = Pi/2. - Vaclav Kotesovec, Feb 07 2015

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Tan[Sec[x]ArcSin[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Nov 26 2014 *)

Crossrefs

Sequence in context: A193185 A359647 A322625 * A012818 A078450 A193502

Adjacent sequences: A012782 A012783 A012784 * A012786 A012787 A012788

Keyword

nonn

Author

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

Status

approved