How to get a sigma style result from Series[]?

[bmmmburns (Marvin Ray Burns A.G.S. (cum laude))]

I use Series[] a lot, but would like the output to the equivalent to Series[Sin[x], {x, Infinity, 0}] to be like.

[mariuszi28cg (Mariusz Iwaniuk)]

Try:

Asymptotic[Sin[x], {x, 0, Infinity}] /. \[FormalN] -> k