"loud laughter," 1620s, from Latin cachinnationem (nominative cachinnatio) "violent laughter, excessive laughter," noun of action from past participle stem of cachinnare "to laugh immoderately or loudly," of imitative origin. Cf. Sanskrit kakhati "laughs," Greek kakhazein "to laugh loudly," Old High German kachazzen, English cackle, Armenian xaxanc'.
cachinnation cach·in·na·tion (kāk'ə-nā'shən)
Loud, hard, or compulsive laughter without apparent cause.