Question 252353
Wow, good question!

I got 26,527,650 using Pascal's triangle and some shortcuts.

Every term is a multiple of 6 (it must have at least one multiple of 3 and an even number in the product) so I started by dividing those out. The sequence that came out was:

1, 4, 10, 20, 35, ...

which I recognised as the 4th diagonal of Pascal's triangle. The sequence of their sums is 1, 5, 15, 35, 70, ..., which is the 5th diagonal.

The sum to 100 terms is the 100th term of that sequence, which is 103C99 = 103C4 = 4,421,475. But remember, we have to multiply that by six to get 26,527,650.