and what do you think about this lense, thank you
Unfortunately, it will not autofocus on the D40. The D40 requires Nikon AF-S designated lenses or Sigma HSM designated lenses.
Nikon makes a 55-200 VR lens which will autofocus and a non-VR 55-200mm, as does Sigma. Link to Sigma:
http://www.sigmaphoto.com/lenses/lenses_all_details.asp?id=3326&navigator=6
Nikon also makes a 70-300mm AF-S lens that will autofocus, if you want the 300mm focal length:
http://www.nikonusa.com/template.php?cat=1&grp=5&productNr=2161
The 70-300mm focal length lenses are pretty much identical. The performance differences (other than AF compatibility) are that Sigma’s glass tends to be much warmer than Nikon’s look, which is neutral to cool. I often prefer the Nikon look, but I will buy third party lenses if they offer something I can’t find in a Nikon lens, like a particular focal length or good performance for the price. For example, the Sigma 80-400 optically stabilized lens performs as well or better than its Nikon equivalent, it’s cheaper, and it will AF on your D40 because it has a built-in focus motor. Another example: Sigma makes a 50-500mm lens that has no Nikon equivalent.
Sorry, no secret compartments or features built into any Sigma lenses…but if you’re buying lenses for "secret" features that nobody knows about…you’d probably believe just about anything then. All of the major third party lens makers, Sigma, Tamron and Tokina have always stood by their lenses, and their quality is quite good. Tokina was founded by former Nikon lens designers for example. I also wouldn’t quote Ken Rockwell, because he’s known for testing cameras by reading the specs and, get this, imagining how they would perform based on the specs and not actual hands on testing. Beware of any one who quotes Ken Rockwell.

Forget about it.
Get a used Nikon lens if you want to save money.
Here is why; from Ken Rockwell:
"Nikon often includes secret features in cameras and in lenses to make them compatible with the next five years or so of secretly planned technology.
For instance, the 1988 F4 is completely compatible with AF-I and AF-S lenses which didn’t appear until 1992 and 1998.
Nikon AI lenses in 1977 already had secret lugs on the back which couple lens information to cameras for Matrix metering, not introduced until the FA of 1983.
Zoom AF lenses, ever since they were introduced in 1986, have always had focal length encoders which insert data into today’s digital cameras’ EXIF data.
AF lenses of today (mockingly even the G versions) still have mechanical lugs for backwards compatibility with the matrix meter of the 1983 FA, and manual focus lenses still have prongs for coupling to the 1959 F."
And … http://www.kenrockwell.com/tech/lens-or-camera.htm
References :
digiPro
OldTimer