Sayyidah Umm Salamah (may Allah be pleased with her) narrates from the Prophet (peace and blessings be upon him) concerning the aqiqah that he (peace and blessings be upon him) said: "Whoever has a child born to him and would like to offer a sacrifice on its behalf, let him do so."
Al-Tabarani recorded it in al-Mu'jam al-Awsat; its chain contains a narrator, Isma'il bin Muslim al-Makki, and he is da'if (weak).