We present deep 3500$-$10000 $AA$ spectra of H II regions and planetary nebulae (PNe) in the starburst irregular galaxy NGC 4449, acquired with the Multi Object Double Spectrograph at the Large Binocular Telescope. Using the direct method, we derived the abundance of He, N, O, Ne, Ar, and S in six H II regions and in four PNe in NGC 4449. This is the first case of PNe studied in a starburst irregular outside the Local Group. Our H II region and PN sample extends over a galacto-centric distance range of $approx$2 kpc and spans $approx$0.2 dex in oxygen abundance, with average values of $12+log(O/H)=8.37 pm 0.05$ and $8.3 pm 0.1$ for H II regions and PNe, respectively. PNe and H II regions exhibit similar oxygen abundances in the galacto-centric distance range of overlap, while PNe appear more than $sim$1 dex enhanced in nitrogen with respect to H II regions. The latter result is the natural consequence of N being mostly synthesized in intermediate-mass stars and brought to the stellar surface during dredge-up episodes. On the other hand, the similarity in O abundance between H II regions and PNe suggests that NGC 4449 s interstellar medium has been poorly enriched in $alpha$ elements since the progenitors of the PNe were formed. Finally, our data reveal the presence of a negative oxygen gradient for both H II regions and PNe, whilst nitrogen does not exhibit any significant radial trend. We ascribe the (unexpected) nitrogen behaviour as due to local N enrichment by the conspicuous Wolf-Rayet population in NGC 4449.
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