What is the pattern rule for 1-4-9-16-15-36 pattern?

Answer 1

assuming you mis-typed the 15 and instead it should be a 25, these are simply the squares of the number's position in the line.

12 = 1

22 = 2

32 = 9

42 = 16

52 = 25 (assume is what you meant)

62 = 36

You can also think of it as adding on the next in a series of odd numbers

1+3 = 4

4+5 = 9

9+7 = 16

which results from expanding (x+1)2 - x2 anyway