Pascal’s triangle is an infinite triangular array of the binomial coefficients.
These numbers are the binomial coefficients used in binomial expansion.
For each row, the row number is and the column number is , where:
The second number of each row is equal to its row number.
The second number of each row has a column number of 1.
The combination function is used to calculate a value in Pascal’s triangle with row number and column number
Figure: rows 0 to 7 of Pascal’s triangle
Figure: rows 0 to 7 of Pascal’s triangle, represented in combinations
Symmetry shows that .
Pascal’s rule (also Pascal’s formula or Pascal’s identity) states that