A012131 cosh(arcsin(tanh(x)))=1+1/2!*x^2-3/4!*x^4+21/6!*x^6-263/8!*x^8...

1, 1, -3, 21, -263, 4841, -99723, -199939, 501445617, -101818966319, 19731909099757, -4192563651606299, 1009030667701246697, -277080625752723191879, 86724157841631252590437, -30813037783471577493355059, 12363651257099764677344554977

Offset: 0

Author

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

Keywords

• sign

Programs

Mathematica

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 *)

Formula

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.

Extensions

More terms from Harvey P. Dale, Mar 08 2015