A013494 exp(arcsinh(x)-arctanh(x)) = 1-3/3!*x^3-15/5!*x^5+90/6!*x^6-945/7!*x^7...

1, 0, 0, -3, 0, -15, 90, -945, 2520, -36855, 368550, -5145525, 31808700, -541215675, 7577019450, -134726216625, 1338322986000, -27408165159375, 493346972868750, -10700744687758125, 147490229469082500

Offset

0,4

Links

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

Formula

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

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

Mathematica

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

Crossrefs

Sequence in context: A013490 A013351 A013407 * A375586 A375557 A375167

Adjacent sequences: A013491 A013492 A013493 * A013495 A013496 A013497

Keyword

sign

Author

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

Status

approved