Low pass and High pass filter Coefficient
To elaborate a bit on Fat32's answer: the most straightforward thing to do is to compute (or estimate) the following two sums:

$$H(e^{j 0})=\sum_nh[n]\tag{1}$$

and

$$H(e^{j \pi})=\sum_n(-1)^nh[n]\tag{2}$$

where $(1)$ is the value of the frequency response at DC (i.e., $\omega=0$), and $(2)$ is the value of the frequency response at Nyquist (i.e., at $\omega=\pi$).

A low pass filter should have a relatively large value for $(1)$ and a very small value (ideally zero) for $(2)$. For a high pass filter the opposite is the case. If both values are small (and if $h[n]$ is not zero) then it's probably a band pass filter, and if both values are relatively large, it's probably a band stop filter. This of course only applies if you can assume that the filter approximates some standard frequency selective filter characteristic.