A012318 - OEIS

%I #11 Feb 06 2015 09:13:48

%S 0,1,2,6,32,240,2000,19656,221888,2846784,40430848,632914304,

%T 10802538496,199980939392,3985563555584,85138224664832,

%U 1939700554334208,46962544699670528,1203843275552612352

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

%F 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

%t CoefficientList[Series[Tan[E^x*ArcSin[x]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Feb 06 2015 *)

%K nonn

%O 0,3

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

%E a(0)=0 prepended by _Vaclav Kotesovec_, Feb 06 2015