A009697 Expansion of tan(tan(x))*exp(x).

0, 1, 2, 7, 20, 117, 518, 4555, 27432, 317577, 2405194, 34316335, 312554428, 5287957053, 56240197198, 1099518892339, 13369846932560, 296443784525713, 4056020122211730, 100546719214082775, 1528702557462347620

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) ~ n! * 4 * ((-1)^(n+1) + exp(2*arctan(Pi/2))) /((4+Pi^2) * exp(arctan(Pi/2)) * arctan(Pi/2)^(n+1)). - Vaclav Kotesovec, Jan 23 2015

Mathematica

Tan[ Tan[ x ] ]*Exp[ x ]
CoefficientList[Series[E^x*Tan[Tan[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)

Crossrefs

Sequence in context: A171191 A189771 A260504 * A139012 A132605 A088157

Adjacent sequences: A009694 A009695 A009696 * A009698 A009699 A009700

Keyword

nonn,easy

Author

R. H. Hardin

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.

Status

approved