Sum of double exponentials with different patterns.

Question

Is there a formula for this expression without using sum? $$f(x) = \sum^x_{i=0}{2^i\cdot3^{i(i+1)/2}} = 2^0\cdot3^0 + 2^1\cdot3^1 + 2^2\cdot3^3+ 2^3\cdot3^6+ 2^4\cdot3^{10} + . . . + 2^x\cdot3^{x(x+1)/2}$$