You can do this with a formula based on the megapixels. I don't know what camera you have but let's say it's 24MP and I am assuming you are using a full frame camera, otherwise that 400mm lens will have a different FOV depending on exactly the camera body you are using - for example 600mm or 640mm if it's an APS-C body. Also note all lens focal lengths are rated at infinity focus, and magnification changes near minimum focus distance are common and can result in a different effective focal length depending on lens design.
This how the math works:
(Desired focal length / actual focal length) squared
Then take your megapixel count and divide it by that value.
EXAMPLE Now let's say you want to see what 600mm would be like, using your 400mm lens and your 24MP full frame camera (feel free to correct my assumptions). Find something far in the distance to take a picture of to eliminate any magnification change caused by the specific lens design.
600/400 = 1.5. Square that (resolution is a square function) and you get 2.25. Now divide your megapixels by 2.25 (24 / 2.25) and you get 10.67MP.
Go into your editor of choice and make a 3:2 crop (the aspect ratio of a full frame camera sensor) that gives you a ~10MP final image. Crop wherever you want and that is what the image would look like if taken with a 600mm lens instead of a 400mm lens. Hope I explained that clearly.
I really like this company:
https://www.zno.com
They have deals all the time, so never pay full price (as with most printing services). The printing is done in China, just in case that bothers you, but shipping is usually 1-2 days so in that respect the distance doesn't matter (assuming you're in North America).
The books I like from them are the Flush Mount albums which allow for a seamless panorama to be printed across 2 pages, and all photos are mounted to foam core which makes a really premium feeling book. The downside of the foamcore is that number of pages are limited if you were hoping for a lot. They have other options as well and offer free sample books if you want to do a test.
The reasons why I don't like the really cheap books other than lower quality "magazine style" press printing is that most of the ones I've ordered have warped. There is often a humidity difference between where you live and where the printing is done and that can cause issues. I usually order fairly large coffee table style books though, so warping is a bigger problem with those than it is for smaller books. Quality wise, as long as the photos are going on good quality paper and being done by an actual printer (not a press), you should be fine.
Anyway, just another option to look at.