He is not sure whether he said the opening takbeer or not
Question

                I entered the mosque and the imam was sitting for the first tashahhud. I joined him in the prayer, but I forgot whether I said the opening takbeer or not.
Praise be to Allah.The opening takbeer is 
    one of the pillars or essential parts of the prayer, which is not waived 
    because of forgetting or not knowing about it, and it cannot be substituted 
    with anything else. If a person remembers during his prayer that he forgot 
    to say the opening takbeer, or he is not sure whether he said it, he has to 
    start the prayer over again. If his doubt about that comes after the prayer, 
    then it does not matter, because doubts after completing an act of worship 
    do not affect it. 

    Based on this, if the doubt of this worshipper who is not 
    sure whether he said the opening takbeer or not came during the prayer, he 
    has to stop praying and start the prayer over again. If the doubt came after 
    the prayer, then he does not have to do anything and his prayer is valid. 

    The evidence that the opening takbeer is an essential part of 
    the prayer is the report narrated by al-Bukhaari (757) and Muslim (397) from 
    the hadeeth of the one who prayed badly. The Prophet  (peace and 
    blessings of Allaah be upon him) said to him: "Go back and pray, for you 
    have not prayed.” Then he said: “When you stand up to pray, say takbeer then 
    recite whatever you know of the Qur'aan. Then bow until you are at ease in 
    bowing, then stand up until you are standing up straight. Then prostrate 
    until you are at ease in prostration, then sit up until you are sitting up 
    straight, and do that throughout your prayer." 

    And Abu Dawood (61), al-Tirmidhi (3) and Ibn Maajah (275) 
    narrated that 'Ali (may Allaah be pleased with him) said: The Messenger of 
    Allaah  (peace and blessings of Allaah be upon him) said: “The key to 
    prayer is purification, its opening is to say Allaahu akbar and its 
    closing is to say al-salaamu’ alaykum.” Classed as saheeh by 
    al-Albaani in Saheeh Abi Dawood. 

    Al-Nawawi (may Allaah have mercy on him) said: 
The opening takbeer is 
    one of the pillars (essential parts) of prayer without which the prayer is 
    not valid. This is our view and the view of Maalik, Ahmad and the majority 
    of earlier and later scholars. Ibn al-Mundhir and our companions narrated 
    that al-Zuhri said: The prayer begins simply with the intention, without any 
    takbeer. But Ibn al-Mundhir said: No one said that except al-Zuhri. 
Then he said: We have 
    stated that the prayer is not valid without the opening takbeer. If the imam 
    or the person praying behind him omits it by mistake or deliberately, his 
    prayer has not begun, and the takbeer for bowing does not make up for it, 
    neither does any other takbeer. This is our view and is the view of Abu 
    Haneefah, Maalik, Ahmad, Dawood and the majority. 

    End quote from al-Majmoo', 3/250 

    Whoever is not sure whether he has said the opening takbeer 
    or not should assume that he has not said it. Shaykh Ibn Baaz said: 

    If a person forgets to say the opening takbeer or is not sure 
    about that, then he has to say takbeer straight away, and follow the imam in 
    whatever comes after he said this takbeer. If he said the takbeer after the 
    imam has done the first rak'ah, then he should regard himself as having 
    missed the first rak'ah, which he should make up after the imam says the 
    salaam. If he said the takbeer in the third rak'ah, then he should regard 
    himself as having missed two rak'ahs, which he should make up after the imam 
    says the salaam. This applies if he is not affected by waswasah (whispers 
    from the Shaytaan). If he is affected by waswasah, then he should regard 
    himself as having said the opening takbeer at the beginning of the prayer, 
    and not make up anything, in order to annoy the Shaytaan and combat his 
    whispers. Praise be to Allaah. End quote. 

    Fataawa al-Shaykh Ibn Baaz, 
    11/275 
If the doubt comes after 
    finishing the prayer, then he should not pay any attention to it. 

    Ibn Rajab (may Allaah have mercy on him) said: If a person is 
    uncertain after finishing a prayer or any other act of worship as to whether 
    he omitted a essential part of it, he should not pay any attention to that 
    doubt. 

    End quote from al-Qawaa'id, p. 340 

    See also the answer to question no. 
    211 

    And Allaah knows best.