How can I prove the following?

1-x+x^2+x^5-x^7-x^12+x^15-x^22-x^26+x^35-x^40+...

= Product[(1 - x^(8 i - 7)) (1 + x^(8 i - 6)) (1 + x^(8 i - 5)) (1 + x^(8 i - 4)) (1 + x^(8 i - 3)) (1 + x^(8 i - 2)) (1 - x^(8 i - 1)) (1 - x^(8 i))] Where the product is from i=1 to infinity.

It doesn't seem to follow from the Triple Product formula and I haven't been able to come up with a combinatorial proof.