The imam combines "Sami' Allahu liman hamidah" and "Rabbana laka al-hamd", and so does the follower

(a) It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that when the Messenger of Allah (peace and blessings be upon him) said 'Sami'allahu liman hamidah' (Allah has heard the one who praised Him), he would also say 'Allahumma rabbana lakal-hamd' (O Allah, our Lord, to You belongs all praise); when he bowed he said the takbir, when he raised his head he also said the takbir, and when he stood up from the two rak'ahs he said 'Allahu akbar' (Allah is the Greatest).
(b) From the word 'kana' (he used to) in this hadith it is understood that he (peace and blessings be upon him) always did this.
(c) In this hadith, the takbir when raising the head means that he (peace and blessings be upon him) said the takbir when, having raised his head from bowing, he went down towards prostration, and Allah knows best. This is explained in another hadith which Abu Bakr bin Abd al-Rahman narrates from Sayyiduna Abu Hurayrah (may Allah be pleased with him).
(d) It has been narrated from Sayyiduna Hudhayfah bin al-Yaman (may Allah be pleased with him) that he too prayed with the Messenger of Allah (peace and blessings be upon him). When he (peace and blessings be upon him) raised his head from bowing, he said 'Sami'allahu liman hamidah' (Allah has heard the one who praised Him), 'Allahumma rabbana lakal-hamd' (O Allah, our Lord, to You belongs all praise).

It is narrated from Hudhayfah (may Allah be pleased with him): I prayed with the Messenger of Allah (peace and blessings be upon him) in the month of Ramadan. When he (peace and blessings be upon him) raised his head from bowing, he said: 'Sami'allahu liman hamidah, Allahumma rabbana wa lakal-hamd' (Allah has heard the one who praised Him. O Allah, our Lord, Yours alone is the being worthy of all praise).

It is reported from Sayyiduna Ali (may Allah be pleased with him) that when he said 'Sami'allahu liman hamidah', he would also recite: 'Allahumma rabbana lakal-hamd, Allahumma bi-hawlika wa quwwatika aqumu wa aq'ud' (O Allah, our Lord, all praise belongs to You. O Allah, by Your might and strength I stand and I sit).

It is narrated from Sa'id bin Abi Sa'id that he heard Abu Hurayrah (may Allah be pleased with him), while he was leading the congregation, say (on rising from bowing) 'Sami'allahu liman hamidah' (Allah has heard the one who praised Him), 'Allahumma rabbana lakal-hamd' (O Allah, our Lord, to You belongs praise), then he said 'Allahu akbar' (Allah is the Greatest). He (may Allah be pleased with him) would say these words in a loud voice, and we would say them too, following him.

(a) It is narrated from Ibn Awn that Muhammad bin Sirin (may Allah have mercy on him) said: When the imam says 'Sami'allahu liman hamidah' (Allah has heard the one who praised Him), those behind him should say: 'Sami'allahu liman hamidah' (Allah has heard the one who praised Him).
(b) It is narrated from Abu Burdah bin Abi Musa that he used to say behind the imam 'Sami'allahu liman hamidah' (Allah has heard the one who praised Him).
(c) Ata' said: The preferred practice in my view is that he combines the two along with the imam.
Two weak (da'if) hadiths have also been narrated on this; I have recorded them in al-Khilaf.