Even after reading this, I don't understand what pi has to do with 4, 20, 56, 120, 220, 364
There's a typo in the final line of math. I think 1/7C2 should be positive rather than negative.
I wonder if the triangle hides any secrets related to prime numbers as well.
π - 2 = 1/1 + 1/3 - 1/6 - 1/10 + 1/15 + 1/21 - 1/28 •••
That's beautiful. I wonder why the -2 is there, though. To fix it, we would need
π = -x + 1/1 + 1/3 - 1/6 - 1/10 + 1/15 + 1/21 - 1/28 •••
where x = 2, and so it would be
π = -1/½ + 1/1 + 1/3 - 1/6 - 1/10 + 1/15 + 1/21 - 1/28 •••
which makes the -1st triangle number ½, I guess.