# Columns of Pascal's Triangle contain Simplicial Polytopic Numbers

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## Theorem

The columns of Pascal's triangle contain the simplicial polytopic numbers:

- Column $0$: repeated instances of number $1$

and so on.

## Proof

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $35$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $35$