the particular supplication for the deceased: “O Allah, forgive him and have mercy on him.”
This arrangement is the same as the order observed in the tashahhud: we begin with al-taḥiyyāt lillāh, which is praise of Allah; then we send salutations upon the Prophet ﷺ; then salutations upon oneself and upon the righteous servants of Allah. The invocation for the deceased is likewise structured, except that here we start with what is general before the specific, whereas in the tashahhud the specific precedes the general, for in the tashahhud you pray for yourself—“peace be upon us”—and a person naturally gives precedence to himself over others, save for the Prophet ﷺ.
To summarise: in the funeral prayer one pronounces the first takbīr, then says, “I seek refuge with Allah from Satan the accursed,” and recites al-Fātiḥah in full. He then utters the second takbīr and invokes blessings upon the Prophet ﷺ. The finest wording is what the Prophet taught his community: “O Allah, bless Muhammad and the family of Muhammad just as You blessed Abraham and the family of Abraham; You are indeed Praiseworthy, Glorious. O Allah, bestow Your favour upon Muhammad and the family of Muhammad just as You bestowed Your favour upon Abraham and the family of Abraham; You are indeed Praiseworthy, Glorious.” After that he pronounces the third takbīr and supplicates for the Muslims at large, saying, “O Allah, forgive…”