pronoun, nominative/accusative neuter plural + enclitic particle
Analysis. tāni (neuter plural of ta 'that') + api ('even', 'also') — 'those very things', 'and even those'. The enclitic api emphasizes or adds the pronoun.
Etymology. ta is the demonstrative pronoun from Indo-European *to- (cognate with English 'the', German 'das', Latin 'tu-' in tu-us). The -ni ending marks neuter plural accusative. api is an enclitic from Indo-European *-pe or *-bhe, a particle of emphasis and conjunction, akin to Greek -pe and Latin -que ('and').
Meanings from the Digital Pāḷi Dictionary; morphology and etymology by Claude.
Lite mode — plain HTML for e-readers and old browsers. Full version