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%I #10 Mar 08 2015 17:52:11
%S 1,1,-3,21,-263,4841,-99723,-199939,501445617,-101818966319,
%T 19731909099757,-4192563651606299,1009030667701246697,
%U -277080625752723191879,86724157841631252590437,-30813037783471577493355059,12363651257099764677344554977
%N cosh(arcsin(tanh(x)))=1+1/2!*x^2-3/4!*x^4+21/6!*x^6-263/8!*x^8...
%F Observe that arcsin(tanh(x)) = int {0..x} 1/cosh(t) so the generating function for this sequence is cosh( int {0..x} 1/cosh(t) ). Note the similarity to the generating function for A000364: cosh( int {0..x} 1/cos(t) ) = 1+x^2/2!+5*x^4/4!+61*x^6/6!+... - Peter Bala, Aug 24 2011.
%t With[{nn=30},Take[CoefficientList[Series[Cosh[ArcSin[Tanh[x]]],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Mar 08 2015 *)
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E More terms from _Harvey P. Dale_, Mar 08 2015