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

0,3

Links

Table of n, a(n) for n=0..16.

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.

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 *)

Crossrefs

Sequence in context: A349961 A251573 A265002 * A322224 A221094 A098278

Adjacent sequences: A012128 A012129 A012130 * A012132 A012133 A012134

Keyword

sign

Author

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

Extensions

More terms from Harvey P. Dale, Mar 08 2015

Status

approved