Option 1: French - The French did have a settlement on the Eastern Coast of India. They established Pondicherry as their main settlement in the 17th century.

Option 2: Portuguese - The Portuguese did have a settlement on the Eastern Coast of India. They were one of the first European powers to arrive in India and established colonies in Goa, Mangalore, and other areas along the coast.

Option 3: Dutch - The Dutch did have a settlement on the Eastern Coast of India. They established colonies in regions such as Pulicat and Negapatam.

Option 4: Danish - This is the correct answer. The Danish did not have a settlement on the Eastern Coast of India. They primarily had settlements in the Tranquebar region on the southeastern coast of Tamil Nadu.

In summary, among the given options, the Danish were the only European colonizers who did not have a settlement on the Eastern Coast of India.