Is the death of an infant after being left asleep and rolling onto its face considered accidental killing, and is expiation obligatory, and what is its measure?

It appears that you did not commit any negligence that led to the death of the child, nor did you directly kill him or cause his death. Therefore, you are not liable for any guarantee, nor are you required to offer expiation, nor is your 'Aqilah (male relatives on the father's side) obligated to pay the blood money. Ibn Hazm said: "If the child dies by the action of his mother, she must offer expiation, and her 'Aqilah or the public treasury must pay the blood money. If he does not die by her action, then nothing is incumbent upon her. If she is in doubt, then there is no blood money and no expiation." It also states in the fatwas of the Permanent Committee that the parents must offer expiation for accidental killing if they placed the sheet and blanket over the child's face and caused her death.