Numerous sets of narrowband filter photometry were obtained of Comet 17P/Holmes from Lowell Observatory during the interval of 2007 November 1 to 2008 March 5. Observations began 8 days following its extreme outburst, at which time the derived water production rate, based on OH measurements, was 5 × 10²⁹ molecule s^–1 and the derived proxy of dust production, A(θ)fρ, was about 5 × 10⁵ cm. Relative production rates for the other gas species, CN, C₂, C₃, and NH, are consistent with "typical" composition (based on our update to the classifications by A'Hearn et al.). An exponential decay in the logarithm of measured production rates as a function of time was observed for all species, with each species dropping by factors of about 200-500 after 125 days. All gas species exhibited clear trends with aperture size, and these trends are consistent with larger apertures having a greater proportion of older material that was released when production rates were higher. Much larger aperture trends were measured for the dust, most likely because the dust grains have smaller outflow velocities and longer lifetimes than the gas species; therefore, a greater proportion of older, i.e., higher production dust is contained within a given aperture. By extrapolating to a sufficiently small aperture size, we derive near-instantaneous water and dust production rates throughout the interval of observation, and also estimate values immediately following the outburst. The finite lifetime of the gas species requires that much higher ice vaporization rates were taking place throughout the observation interval than occurred prior to the outburst, likely due to the continued release of icy grains from the nucleus. The relatively small aperture trends for the gas species also imply that the bulk of fresh, excess volatiles are confined to the nucleus and near-nucleus regime, rather than being associated with the outburst ejecta cloud. A minimum of about 0.1% of the total nucleus volume was vaporized water ice, while a dust volume corresponding to at least 1%-2% was likely to have been released from the nucleus.