The Sunnah of praising Allah after eating

Khalid bin Ma'dan relates: I attended a wedding feast (walimah) at the house of Abd al-A'la, and Sayyiduna Abu Umamah al-Bahili (may Allah be pleased with him) was with us. When we had finished eating, he stood up and said: "I do not wish to be a preacher, but I heard the Messenger of Allah (peace and blessings be upon him) saying, when he finished eating: 'Al-hamdu lillahi kathiran tayyiban mubarakan fihi, ghayra muwadda'in wa la mustaghnan 'anhu' (All praise is for Allah, praise that is abundant, pure and blessed, which is never abandoned and which one can never do without)."
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs did not record it, and its supporting narration (shahid) exists with narrators who are more authentic and better known than those of this one.

It is narrated from Sayyiduna Abu Umamah (may Allah be pleased with him) that when the dining cloth was lifted from before the Messenger of Allah (peace and blessings be upon him), he (peace and blessings be upon him) would supplicate: 'Al-hamdu lillahi hamdan kathiran tayyiban mubarakan fihi, ghayra muwadda'in wa la mustaghnan 'anhu, rabbana' (All praise is for Allah, praise that is abundant, pure and blessed, which can neither be bidden farewell nor ever be done without, O our Lord!).

It is narrated from Sayyidah Aishah (may Allah be pleased with her) that she said: We had a goat, and we feared it would die, so we slaughtered it and distributed all of it (in charity) except the meat of its shoulder.
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs did not record it.