Is the imam's prayer valid if he doubts the number of rak'ahs and does not perform the prostration for forgetfulness?

The questioner:
May Allah reward you, Honorable Shaykh. This questioner says: An imam doubted the number of rak'ahs and did not perform the prostration for forgetfulness. When he asked the ma'mums after the prayer, they confirmed the completion of the prayer and that they had not alerted him.

The Shaykh:
Did they confirm what?

The questioner:
The completion of the prayer.

The Shaykh:
Probably, yes, yes.

The questioner:
So is his prayer valid if he left the prostration for forgetfulness because of his doubt?

The Shaykh:
Nothing was more likely in his mind. Yes, because the prostration for forgetfulness is obligatory for doubt to rectify the prayer, but one is excused by ignorance, or if the interval is long. If he is ignorant, he is excused by ignorance, or if he is knowledgeable but the interval is long, meaning it is dropped. Yes.