He did the first sajdah of sujood al-sahw, then he remembered that he did not do anything that required sujood al-sahw. Should he do the second sajdah or not?

Praise be to Allaah. 

Shaykh
‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) was asked this
question, and he hesitated, then he replied:

 The
best thing is for him to do the second sajdah, so as not to confuse people
and give them cause to shout “Subhaan
Allaah
” [to draw his attention to his mistake] – that is, if he is the imaam. And Allaah knows best.