Is it permissible to combine the intention of the 'aqiqah for oneself and for one's son in a single 'aqiqah?

'Aqiqah (definition) is a confirmed Sunnah (definition) for the father. And he who did not perform 'Aqiqah for his young son who passed away, that son will not intercede for his father, according to one of the two interpretations of the Hadith (definition), "Every child is a pledge for his 'Aqiqah." Performing 'Aqiqah for oneself after puberty is contrary to the Sunnah according to Imam Ahmad, while Imam Shafi'i permitted it. If you wish to perform 'Aqiqah for yourself, the 'Aqiqah of your son will not suffice; rather, an independent 'Aqiqah is necessary, in which what suffices for Udhiyah (definition) (sacrifice) will suffice.