We propose the notation $ñ(m,k)$ for the number of partitions of $m$ points into $k$ sets that can be empty. We needed a notation since we proved (in [this paper][1]) some relations for this kind of partitions. 


  [1]: https://doi.org/10.1007/s40590-022-00478-9 "Arciniega-Nevárez, J.A., Berghoff, M. & Dolores-Cuenca, E.R. An algebra over the operad of posets and structural binomial identities. Bol. Soc. Mat. Mex. 29, 8 (2023)."