0,1,4,9,16,25,36,49,64,81,100,121,144,169

1,3,5,7, 9 ,11,13, and you see where this is going. All the numbers in this row are odd numbers, two different.

What about cubed...

0, 1 , 8 , 27,64,125,216,343,...

1, 7 ,19,37 ,61, 91 ,127,... (continuing)

6,12,18,24 ,30, 36 , and now we have six different.

Now here, I went to the 4th power:

0 , 1 , 16 , 81 ,256,625,1296,2401,...

1 ,15, 65 ,175,369,671,1105,...

14,50,110,194,302,434,...

36,60, 84 ,108,132,...

24,24, 24 , 24 , and now we have 24.

0th power does this:

0,0,0,0,0,...

0,0,0,0,... (you get it)

1st power is this:

0,1,2,3,4,5,6,...

1,1,1,1,1,1, and now 1s.

Next, I arranged them like this:

0,1,2,6,24,...

And before I go on, I would like to note something. From one onward, if you multiply the 1 by two, you get the next object in the sequence, 2. 2*3=6, 6*4=24. I have confirmed this up until the multiplication by seven. So why is 0*1=1?

Anyway, proceeding:

0 , 1 , 2 , 6 , 24 ,120,720,...

1 , 1 , 4 , 18 , 96 ,600,...

0 , 3 , 14 , 78 ,504,...

3 , 11 , 64 ,426,...

8 , 53 ,362,...

45 ,309,...

264,...

Now, this may be infinite, but, using the information that you gleaned from this, I would like an equation, a possible answer to the 0,1,2,6,24... sequence, and I would like to know a way to submit this as an unsolved problem in math.

This may be unsolvable, just to let you know. It appears that the multiplication rate is higher than the deduction rate. But, this may work against itself. And for right now, I would be happy to leave the answer at, of course, 42.