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This answer shows an extended version of Pascal's Triangle that works for negative numbers too.

In This video, Sal shows how to interpret the members of Pascal's Triangle as the sum of all the possible paths to get to that member.

Is there any way we can use this same 'sum of all the possible paths' to interpret This extended version of Pascal's Triangle?

Plague
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  • Given that answers to counting problems are always non-negative integers... no. – JMoravitz Apr 17 '24 at 13:20
  • If you examine that table for negative $n$, you will see that the form an inverted and rotated Pascal's triangle, if one ignores the sign (as Markus Scheuer points out at the bottom of the post). So the same scheme can be set up in the reverse direction, explaining everything about the numbers except their sign. – Paul Sinclair Apr 18 '24 at 11:39

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