A012587 - OEIS

%I #17 Feb 06 2015 09:17:10

%S 0,1,2,4,24,180,1240,10456,112896,1316816,16378528,229634304,

%T 3569726336,59315089600,1055150016128,20254767489152,415619313491968,

%U 9028238025838848,207506148418183680,5043727679716764672

%N E.g.f.: tan(arcsinh(x)*exp(x))=x+2/2!*x^2+4/3!*x^3+24/4!*x^4+180/5!*x^5...

%F a(n) ~ n! / ((Pi/2 + exp(r)/sqrt(1+r^2)) * r^(n+1)), where r = 0.782048434734397136830260131892318660005898990290325... is the root of the equation arcsinh(r)*exp(r) = Pi/2. - _Vaclav Kotesovec_, Feb 06 2015

%t With[{nn=20},Join[{0},Rest[CoefficientList[Series[Tan[ArcSinh[x]Exp[x]],{x,0,nn}], x]Range[0,nn]!]]] (* _Harvey P. Dale_, May 07 2012 *)

%K nonn

%O 0,3

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