Answer: The Gemara (Kiddushin 29a) writes that if one failed to redeem his son when he was a child, then his son should do so himself. Thus, the Shulchan Aruch (YD 305:15) writes that one who wasn’t redeemed should redeem themselves when they grow up. The Pischei Teshuva (YD 305:25) quotes the Zichron Yosef (YD 26) who stresses that this must wait until he is bar mitzva.
There is a machlokes among the rishonim, however, as to whether the father is still obligated to redeem his son, or whether his grown up son should perform it himself. The Rashba (Shut 2:321) argues that the father’s obligation does not disappear with time. Similarly, the Sefer Hachinuch (392) writes that while the father should ideally perform this mitzva when the baby is thirty days old, the obligation remains even after one’s son has grown up. Thus, the Minchas Chinuch (392:1) writes that as the mitzva belongs primarily to the father, if his son performed it himself, he could be fined ten zehuvim (See Shulchan Aruch CM 382:1).
The Rivash (131), however, writes that once the son turns bar mitzva it becomes his primary obligation, rather than his father’s. As he couldn’t have redeemed himself as a baby, it was then his father’s obligation, but now that he can do so himself, he should.
While R’ Ephraim Greenblatt (Rivevos Ephraim 3:518) writes that we follow the Rashba, R’ Moshe Sternbuch (Teshuvos Vehanhagos 1:370) writes that the Shulchan Aruch implies that we follow the Rivash, and the son should now redeem himself. Nonetheless, he suggests that it is possible for them to both perform the mitzva. The father should give his son the money while his son performs the actual pidyon.
In conclusion, both the father and his grown son are obligated to perform the pidyon haben. As there is a machlokes as to whose obligation is paramount, it is ideal to do the pidyon in a manner that involves them both, so that they can both perform the mitzva.