What sequence of numbers did Ada Lovelace's algorithm compute?

Ada Lovelace's algorithm for Charles Babbage's Analytical Engine was designed to compute Bernoulli numbers. She described it in Note G, the final and most technically detailed section of her 1843 notes.

Bernoulli numbers are a sequence of rational numbers that appear in formulas for sums of powers, calculus, and number theory. They had been studied centuries earlier by mathematicians including Jacob Bernoulli and, independently, the Japanese mathematician Seki Takakazu.

Lovelace’s work was not a program run on a completed machine: Babbage’s Analytical Engine was never built during their lifetimes. Instead, her table and instructions showed how the proposed machine could carry out a complicated sequence of operations using punched cards and stored values.

This is why the achievement is often called the first published computer program, although historians debate how much of the algorithm was Lovelace’s original creation versus Babbage’s contribution. The important historical point is that her notes clearly explained machine-based symbolic computation, not merely simple arithmetic.