A012318 tan(arcsin(x)*exp(x))=x+2/2!*x^2+6/3!*x^3+32/4!*x^4+240/5!*x^5...

0, 1, 2, 6, 32, 240, 2000, 19656, 221888, 2846784, 40430848, 632914304, 10802538496, 199980939392, 3985563555584, 85138224664832, 1939700554334208, 46962544699670528, 1203843275552612352

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) ~ n! / ((Pi/2 + exp(r)/sqrt(1-r^2)) * r^(n+1)), where r = 0.70212550839123612037106419625287862875439228120419... is the root of the equation arcsin(r)*exp(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015

Mathematica

CoefficientList[Series[Tan[E^x*ArcSin[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 06 2015 *)

Crossrefs

Sequence in context: A111550 A261398 A009686 * A012521 A211195 A346452

Adjacent sequences: A012315 A012316 A012317 * A012319 A012320 A012321

Keyword

nonn

Author

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

Extensions

a(0)=0 prepended by Vaclav Kotesovec, Feb 06 2015

Status

approved