He forgot that he did not have wudoo' and he prayed

Praise be to Allah. 

Yes, whoever prays forgetting that he does not have wudoo' has to repeat the prayer, because the Messenger (peace and blessings of Allaah be upon him) said: «Allah does not accept any prayer if a person breaks his wudoo', until he does wudoo'» (Narrated by al-Bukhaari from the hadith of Abu Hurayrah (may Allaah be pleased with him) in Kitaab al-Wudoo').

This is in contrast to the person who has some impurity (najaasah) on his clothes and he forgets it. He does not have to repeat his prayer because Jibreel came to the Prophet (peace and blessings of Allah be upon him) whilst he was praying, and told him that there was something dirty on his shoes. He took them off and continued praying. This was narrated by Ahmad from the hadith of Abu Sa'eed al-Khudri (may Allaah be pleased with him) in his Musnad. This hadith proves that the one who is unaware of the najaasah does not have to repeat his prayer, and this applies also to the one who forgets that there is some najaasah present. 

(I'laam al-Musaafireen bi Ba'd Aadaab wa Ahkaam al-Safar wa ma yakhuss al-Mallaaheen al-Jawwiyyeen by Shaykh Muhammad ibn Saalih al-'Uthaymeen, p. [12]).