Praise be to Allah.
There are fifteen places in the Quraan where we should perform sajdat al-tilaawah (prostration of recitation) when reciting them. It was reported from Amr ibn al-Aas that the Messenger of Allaah (peace and blessings of Allaah be upon him) recited to him fifteen verses in the Quraan where one should prostrate, three of which are in al-Mufassal and two in Soorat al-Hajj. It was reported by Abu Dawood, Ibn Maajah, al-Haakim and al-Daaraqutni, and classed as hasan by al-Mundhiri and al-Nawawi. The fifteen aayat are (interpretation of the meanings):
1 - Surely those who are with your Lord (angels) are never too proud to perform acts of worship to Him, but they glorify His Praise and prostrate before Him.
2 - And unto Allaah (Alone) falls in prostration whoever is in the heavens and the earth, willingly or unwillingly, and so do their shadows in the mornings and in the afternoons.
3 And to Allaah prostrate all that is in the heavens and all that is in the earth, of the live moving creatures and the angels, and they are not proud [i.e., they worship their Lord (Allaah) with humility].
4 Say (O Muhammad): Believe in it (the Quraan) or do not believe (in it). Verily! Those who were given knowledge before it, when it is recited to them, fall down on their faces in humble prostration.
5 When the Verses of the Most Beneficent (Allaah) were recited unto them, they fell down prostrating and weeping.
6 See you not that to Allaah prostrates whoever is in the heavens and whoever is on the earth, and the sun, and the moon, and the stars, and the mountains, and the trees, and al-dawaab (moving living creatures, beasts, etc.), and many of mankind? But there are many (men) on whom the punishment is justified. And whomsoever Allaah disgraces, none can honour him. Verily! Allaah does what He wills.
7 O you who believe! Bow down, and prostrate yourselves, and worship your Lord and do good that you may be successful.
8 And when it is said to them: Prostrate to the Most Beneficent (Allaah)! They say, And what is the Most Beneficent? Shall we fall down in prostration to that which you (O Muhammad) command us? And it increases in them only aversion.
9 [As Shaytaan has barred them from Allaahs Way] so that they do not worship (prostrate before) Allaah, Who brings to light what is hidden in the heavens and the earth, and knows what you conceal and what you reveal.
10 Only those believe in Our aayaat (verses, signs, etc.) who, when they are reminded of them fall down prostrate, and glorify the Praises of their Lord, and they are not proud.
11 And Dawood guessed that We had tried him and he sought forgiveness of his Lord, and he fell down prostrate and turned (to Allaah) in repentance.
12 And from among His Signs are the night and the day, and the sun and the moon. Prostrate not to the sun nor to the moon, but prostrate to Him Who created them, if you (really) worship Him.
13 So fall down in prostration to Allaah, and worship Him (Alone).
14 And when the Quraan is recited to them, they fall not prostrate.
15 Fall prostrate and draw near to Allaah!
Al-Albaani said, in Tamaam al-Minnah (296):
On the contrary, the hadeeth is not hasan, because it includes two majhool [unknown] narrators. Al-Haafiz said in al-Talkhees, after quoting the opinion of al-Mundhiri and al-Nawawi that it is hasan: Abd al-Haqq and Ibn Qattaan classed it as daeef [weak]. It includes Abd-Allaah ibn Munayn, who is majhool, and the one who narrated from him is al-Haarith ibn Saeed al-Atqi, who is also unknown. Ibn Maakoolaa said: He did not narrate any hadeeth apart from this one.
Hence al-Tahhaawi was of the opinion that there is no second sajdah in Soorat al-Hajj, towards the end of the soorah. This is also the opinion of Ibn Hazm who said in al-Muhalla:
Because it is not narrated in any saheeh report that this was the Sunnah of the Messenger of Allaah (peace and blessings of Allaah be upon him), and there is no scholarly consensus to this effect. But it was reported with a saheeh isnaad that Umar ibn al-Khattaab, the daughter of Abd-Allaah and Abu Darda performed sajdah in (the second verse quoted from Soorat al-Hajj).
Then Ibn Hazm discussed whether the sajdahs for the other aayaat quoted are prescribed in Islam. He mentioned that the scholars are agreed upon the first ten, that performing sujood when reciting these aayaat is prescribed. Al-Tahhaawi also reported this consensus in Sharh al-Maaani (1/211), but he said that the sajdah in Soorat Fussilat was prescribed, instead of the sajdah in Soorat Saad. Both scholars narrated ahaadeeth with saheeh isnaads from the Messenger of Allaah (peace and blessings of Allaah be upon him) concerning the sajdahs in Saad, al-Najm, al-Inshiqaaq and al-Alaq. These last three are from the Mufassal, which is referred to in the hadeeth of Amr mentioned above.
In conclusion, even though the isnaad of the hadeeth is weak, it is supported by the consensus of the ummah which supports most of it, and by saheeh ahaadeeth which support the rest of it, except for the second sajdah in Soorat al-Hajj, for which there is no evidence in the Sunnah or in the consensus of the scholars. But some of the Sahaabah used to prostrate when reciting it, which could be taken as evidence, especially since no one is known to have disputed with them in this regard.
To sum up, the prostration of recitation should be performed when reciting the fifteen verses quoted above. And Allaah knows best.