A009207 Expansion of exp(sin(x))/cos(x).

1, 1, 2, 3, 8, 17, 88, 315, 2176, 9505, 78080, 413523, 4159616, 26287601, 307882240, 2238416523, 29920681984, 246589091137, 3710767394816, 34186190864163, 571523842998272, 5819027995038161, 107010484096565248

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

E.g.f.: 1/cos(x)+ tan(x)/Q(0), where Q(k) = 4*k+1 -sin(x)/(2 + sin(x)/( 4*k+3 - sin(x)/(2 + sin(x)/Q(k+1) ))); (continued fraction). - Sergei N. Gladkovskii, Dec 08 2013

a(n) ~ n! * (exp(1) + exp(-1)*(-1)^n) / (Pi/2)^(n+1). - Vaclav Kotesovec, Jan 22 2015

Mathematica

Exp[ Sin[ x ] ]/Cos[ x ]
CoefficientList[Series[E^Sin[x]*Sec[x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 22 2015 *)

Crossrefs

Sequence in context: A324963 A218090 A101182 * A290878 A096254 A091765

Adjacent sequences: A009204 A009205 A009206 * A009208 A009209 A009210

Keyword

nonn,easy

Author

R. H. Hardin

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.

Status

approved