עַל־חַטֹּ֤אות יָרָבְעָם֙ אֲשֶׁ֣ר חָטָ֔א וַאֲשֶׁ֥ר הֶחֱטִ֖יא אֶת־יִשְׂרָאֵ֑ל בְּכַעְס֕וֹ אֲשֶׁ֣ר הִכְעִ֔יס אֶת־יְהוָ֖ה אֱלֹהֵ֥י יִשְׂרָאֵֽל׃
a causa dei peccati che Geroboamo aveva commesso e con cui aveva fatto peccare Israele, provocando con la sua provocazione il Signore, Dio d'Israele.
Sforno
פוקד עון אבות, the reason why I sometimes wait so long before punishing some of the wicked in this life is that by waiting and noticing that their offspring, i.e. second and third generation continue in their wicked ways their measure of guilt will become so full that I will exterminate that whole family from life in this world. [this is what happened to the family of Jerobam for instance, and that of Omri, his son Achav, etc. ] This was possible only by adding the unrequited sins of the fathers to those of the sons, or even subsequent generations, so that when finally, retribution did come, it wiped out the family completely. This happened in the third generation of the original sinner such as Omri’s grandchildren. It also happened to the fourth generation after Yehu (who himself had been G’d’s instrument for wiping out the family of Omri/Achav) when his great grandson Zecharyah was murdered after reigning only 6 months. (Kings II 15,9) We know about this method G’d employs sometimes already since Genesis chapter 15 when G’d explained to Avraham that his descendants could not expect to take possession of the land of Canaan until the fourth generation, as the sins of the Emorite would not be irrevocable until then. (Genesis 15,16)
English Explanation of Pirkei Avot
Moses was righteous and caused the multitudes to be righteous, [therefore] the righteousness of the multitudes is hung on him, as it is said, “He executed the Lord’s righteousness and His decisions with Israel” (Deut. 33:21). Jeroboam, sinned and caused the multitudes to sin, [therefore] the sin of the multitudes is hung on him, as it is said, “For the sins of Jeroboam which he sinned, and which he caused Israel to sin thereby” (I Kings 15:30). Moses is the greatest example of leadership that the Jewish people has ever known. He was righteous in his own right and he taught others to be righteous as well. As a reward, the righteous acts that the people performed are accredited to him, as if he himself performed them. The verse in Deuteronomy quoted in the mishnah is understood as referring to Moses (although this is not at all clear from the verse itself). According to the mishnah’s understanding, the verse states that Moses did God’s righteousness, and that all of the acts of Israel were counted as his acts as well. From here we learn that when students perform the righteous acts which they have learned from their teachers, the teachers receive credit themselves. Jeroboam was the first king of the northern kingdom (Israel) when it split from the southern kingdom (Judea) after Solomon’s death. Jeroboam told Israel that they no longer had to go to Jerusalem to worship, but could worship at Bethel as well as other places in the north. He made two golden calves and told the people “This is your god, O Israel, who brought you up from the land of Egypt” (I Kings 12:28). Jeroboam did not only himself sin, but he caused others to sin as well. In I Kings 15:25-30, Baasha son of Ahijah kills Nadav, son of Jeroboam and all of Jeroboam’s house as well (Jeroboam himself had already died). Verse 30 concludes that the Jeroboam’s house was killed on account of Jeroboam and his sin and the sins that he caused Israel to sin. From here we can conclude that Jeroboam himself was held accountable for those sins which he caused others to do.