Disclaimer: I only watched the TV show, I did not read the books.
In Game of Thrones Season 6 Episode 6 (Blood of my Blood), we see Samwell Tarly leaves his father's home and, in the process, steals Heartsbane, which has been the ancestral sword of House Tarly for centuries and one of the very few Valyrian steel swords left in Westeros. This makes it extremely valuable.
We see that this dialogue takes place during the dinner:
Samwell: I traveled south under orders of the Lord Commander. He wants me to...
Randyll: I read your letter. You're to be a... a Maester.
Samwell: Yes. And once I have my chain, I'll return to Castle Black.
Randyll: I thought the Night's Watch might make a man of you. Something resembling a man, at least. You managed to stay soft... and fat. Your nose buried in books. Spending your life reading about the achievements of better men. I'll wage you still can't sit on a horse or wield a sword!
So, we know that Randyll has a very bad relationship with his first-born son, Samwell:
- He sends Sam to the Wall on his 18th birthday, under the threat of death.(Samwell tells Jon about this in Season 1 Episode 4)
- He's disappointed in him because "he's not a real man" and he's fat.
- He's extremely angry at him for bringing a Wildling woman into his house.
There are probably more negative aspects about their relationship that don't come to mind right now. But it's very clear that Randyll basically doesn't care at all for Sam.
That being said: Why didn't Randyll go after Sam in the morning after Sam left with Heartsbane? Or at least send a team of men after him? Randyll knows exactly where Samwell will go, he knows where to find him (see the dialogue above). Therefore, it would be very easy to go after him and take the sword back.
It would make sense, given both the sword's high value and Randyll's "I-don't-give-a-crap-about-you" attitude towards Samwell.
So, why doesn't that happen? Am I missing something?