Descending Stories: Showa Genroku Rakugo Shinju

Showa Genroku Rakugo Shinjuu is a manga by Haruko Kumota. It was adapted into two OVAs then an anime, and was part of the winter 2016 anime season.

Plot
It is the seventies. As soon as Kyoji gets out of prison, he goes to Yakumo Yurakutei the rakugo master. Yakumo performed a play called "Shinigami" in the past, motivating the former criminal to take up rakugo himself. After being accepted by Yakumo with almost no reluctance (despite there being another lodger, a lady called Konatsu), Kyoji must not only learn about rakugo but also about what came before him if he is to quell the tumultuous feelings between Yakumo and Konatsu.

Official
http://rakugo-shinju-anime.jp/