Sherlock is the sole carer of John's newborn daughter after Mary dies

[grypas.livejournal.com]

Hi,

I'm looking for a story where Sherlock cares for John's newborn baby after Mary dies.
I remember that the story starts at the hospital. The baby is left at the neonatal ward and Sherlock fetches her and asks the nurses for instructions on baby formula etc. He is the sole carer of the baby for a long time, John has somehow shut off and is indifferent towards the baby. I think that Sherlock even names her.

I might confuse more than one stories. I remember that Sherlock was fascinated by the baby and kept her with him most of the time. John was drowned in grief and didn't react to the baby crying. I remember that Sherlock took care of both father and child. There was a scene with both John and the baby coming back to Baker Street after the hospital and Sherlock guiding John back inside and upstairs.

I can't believe that I forgot all about it.

Thank you in advance for your answer

ETA: Partially found. The hospital scene is from Just for fun by Littlepippin76.