The corpus, every claim citable.

Mahāvīra's Ganita-sara-sangraha VI.218 (850 CE) gives the general algorithmic statement of the nCr formula: write 1..n ascending and n..1 descending in two rows; the product of the top r entries divided by the product of the bottom r is nCr. Pingala (~200 BCE) had the binomial-prosody special case; Pascal's Traité (1654 CE) gives the European systematic form. Mahāvīra's algorithm is the general procedural statement, 800 years before Pascal.

The Ganita-sara-sangraha of Mahaviracarya · 850

Pingala's Chandahsutra (~200 BCE) gives a four-aphorism recursive algorithm for counting metrical arrangements of n syllables. The rules ("halve; subtract one when odd; multiply by two; square when halved") implement exponentiation-by-squaring — the same recurrence modern computers use to compute 2ⁿ in O(log n) steps. Halayudha's 10th-century commentary makes the recursion explicit. The algorithm predates Leibniz's binary arithmetic (1703) by ~1,900 years.

History of Hindu Mathematics — A Source Book · 1938