A013154 exp(tanh(x)+arcsinh(x)) = 1+2*x+4/2!*x^2+5/3!*x^3-8/4!*x^4-63/5!*x^5...

1, 2, 4, 5, -8, -63, -26, 1311, 4008, -40503, -288486, 1746571, 23670420, -107820971, -2395713498, 11358568591, 304636017840, -2325027955727, -49472656345230, 758733754118995, 10516377983584300

Offset

0,2

Comments

Asymptotic expansion (below) converge much faster if n is odd. If n is even, then more than 1000 terms necessary for right numerical verification. - Vaclav Kotesovec, Nov 01 2013

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Vaclav Kotesovec, graph a(n) / asymptotic

Formula

E.g.f.: (x+sqrt(1+x^2))*exp(tanh(x)). - Vaclav Kotesovec, Nov 01 2013

a(n) ~ -2*cos(Pi*n/2-tan(1)) * n^(n-1) / exp(n). - Vaclav Kotesovec, Nov 01 2013

Mathematica

CoefficientList[Series[Exp[Tanh[x]+ArcSinh[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 01 2013 *)

Crossrefs

Sequence in context: A159260 A013103 A012973 * A013129 A104311 A200818

Adjacent sequences: A013151 A013152 A013153 * A013155 A013156 A013157

Keyword

sign

Author

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

Status

approved