My father has died he had 4 sons one son is deceased what share of of my fathers estate is the deceased sons children legally entitled to?

This cannot be answered without knowing the state involved or whether there is a will or not. Generally, in most states and in New Jersey, where there is no will, the children of a deceased child will inherit the share of the estate that the deceased child would have received and split it equally. This is called taking by representation. When there is a will, you first have to see if it says anything about that situation and if it does, the you follow the will. A will might say that if any child of mine predeceases me then I give that child's chare to my surviving children, or to charity or to whomever he wants. If the will makes no mention of that situation then the grandchildren take by representation just as if there were no will.