I see an even stronger pattern, but . . .I have a set of expressions which are related.
The relationship is apparent in the multipliers in each line.
You have a variation of Pascal's Triangle . . .
Each number is the sum of the two numbers directly above it.
In row 3, we have: which represents the polynomial:
. . and its coefficients are in row 4.
. . Its coefficients are in row 5.
. . Ites coefficients are in row 6.
So I see the powerful pattern embedded in the triangle,
. . but so far, I haven't been able to express this in a closed form.