Another Jaramillo Triangle

In this triangle:
1- The sum of the terms in the rows is equal to the number of terms of the

polynomial factorial: t!
2- The denominator (above) is equal to the number of terms of the initial

polynomial minus one, factorial: (t-1)!
3- The sum of the exponents is equal to (t2+3t+2)/2 where “t” would be

equal to the number of terms of the initial polynomial.
4- The constant term is equal to the denominator.

Note: The numbers in the triangle are the absolute values of the “Stirling Numbers”

of the first kind.