What is the ruling on forgetting the number of days for the delayed making up of Ramadan fasts, and is expiation (fidyah) obligatory along with not remembering the number of days?

If a Muslim deliberately delays making up missed Ramadan fasts without a valid excuse, he is obligated to offer expiation (kaffarah) for each day. As a precautionary measure, he should offer twelve expiations. If he is unsure about the number of days, he should take the lesser, certain number, and it is more cautious to make up the day about which he is doubtful. However, if the delay was due to ignorance or forgetfulness, then no expiation is required of him.