Applying fertilizer at the same time you seed your lawn is not a recommended idea. Many experts will tell you that doing so you could risk to destroy a large part of your lawn where the soil was heavily fertilized. The result could be that your fertilizer will be unevenly distributed and the resulting patchy areas will burn seedlings rather than nourish them.
The best practice, if you want to add some extra nutrition to your lawn while seeding, is to apply a starter best lawn fertilizer, which is typically milder and less destructive.
One of the best methods to apply your starter fertilizer is to stick with 5-10-5 nitrogen, phosphorous, potassium, and apply it carefully at a rate of about half a pound for each 25 square feet of soil. This way you can prevent your lawn from being burned by excess fertilizer and ensure that it still gets good nutrition throughout its growth cycle.
It’s good practice to calculate the rate of applying the fertilizer in advance and use a reliable weighted roller in order to push the seed into the ground after fertilizing. That way you’ll know that the seeds have proper contact with the soil and that they will receive the optimal amount of nutrition from your starter fertilizer.