Patterns in pascal triangle

In Pascal triangle there are various patterns and numbers like natural numbers, triangular numbers, hexagonal numbers, Catalan numbers, sierpienski triangle and many more. Try to explore those patterns and application of Pascal triangle in our daily life.
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Pascal's triangle:

1 Row 0
1 1 Row 1
1 2 1 Row 2
1 3 3 1 Row 3
1 4 6 4 1 Row 4
1 5 10 10 5 1 Row 5
1 6 15 20 15 6 1 Row 6
1 7 21 35 35 21 7 1 Row 7
1 8 28 56 70 56 28 8 1 Row 8