Natsume Yuujinchou: Nyanko-sensei to Hajimete no Otsukai

夏目友人帳新 ニャンコ先生とはじめてのおつかい

This anime DVD has a completely original story not told in the manga or its earlier anime adaptations.

Note: Given to subscribers of LaLa and LaLa DX magazines.

(Source: AniDB)