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We report a $^{139}$La-NMR study on the multiple($n$)-layered nickelatesLa$_3$Ni$_2$O$_7$ ($n=2$) and La$_4$Ni$_3$O$_{10}$ ($n=3$) at ambient pressure.Observations of the broadening in NMR spectra and the anomaly of nuclear spinrelaxation rate ($1/T_1$) indicate the emergence of density wave order with agap below $T^*\sim150$~K for La$_3$Ni$_2$O$_7$ and $\sim130$~K forLa$_4$Ni$_3$O$_{10}$. Below $T^*$, the behavior of $1/T_1T \sim const.$indicates the metallic ground states with remaining density of states (DOS) atthe Fermi level ($E_{\rm F}$) under the density wave order, revealing theexistence of multiple $d$-electron bands with different characters. Above$T^*$, the gradual decrease of $1/T_1T$ upon cooling indicates the presence ofa strong variation of DOS near $E_{\rm F}$. Since this feature disappears wellbelow $T^*$, it is inferred that the density wave gap opens at the bandassociated with this structure in DOS at $E_{\rm F}$. From our microscopicinsights, we point out that these nickelates ($n=2$ and $3$) possess similarelectronic states despite the difference in the formal valence of the Ni$d$-electron states, which provides with basis for understanding the novelhigh-$T_{\rm c}$ superconductivity under high pressures.

Multiband Metallic Ground State in Multilayered Nickelates La$_3$Ni$_2$O$_7$ and La$_4$Ni$_3$O$_{10}$ Revealed by $^{139}$La-NMR at Ambient Pressure