I went down worldpopulationreview.com's list; I'll post my list annotated with country size as a reply to this comment.

Findings:

India, the country, is #28. It has essentially equal population density to the Netherlands (#29, in Europe!), while being a modest 87 times larger. Belgium (#33) has only slightly less density, and India is merely 102 times bigger.

The next European country down is England at #50. It's much closer to the size of India -- 8% as large -- and has two-thirds the density.

Pakistan is #55; it's about four times the size of England with comparable density.

#59 is Germany; it's less than half the size of Pakistan with comparable density. Luxembourg and Liechtenstein, who you might have thought would have super-high density, are equal to Germany. (Monaco and Vatican City really do have super-high density.)

The only other country-sized European countries in the top 70 are Switzerland and Italy, #68 and #69. They have half the density of India. Italy is a tenth of India's size. Switzerland is slightly larger than the Netherlands.

Bangladesh, by the way, is #12, with more than double the density of India (in about 1/20 of the space).

So I can't agree that India's population density is comparable to "many Western European countries". It's comparable to a couple of diminutive European countries. Equal density over 100 times the area is not what you would expect; it's something very unusual about India.

In fact, we can just compare the regions directly. Europe has 743 million people in 10 million square kilometers of land for an average density of 74.3 people per square km. India (including Pakistan and Bangladesh) has 1740 million people in 4 million square km, for an average density of over 400 people per square km (roughly equal to the density of India the country, which makes sense), about 6 times the figure for Europe.