[seqfan] Need help with puzzling sequence A118980

[Neil Sloane]

Dear SeqFans, I have been cleaning up some old sequences with keyword
"uned".
At the end of the weekend, this one is still a mystery: A118980.  The
puzzle boils down to this:
What is the triangle?

1;

2, 1;

6, 5, 2;

14, 22, 18, 6;

34, 85, 118, 84, 24;

82, 311, 660, 780, 480, 120;

...



*All that is needed is a plausible guess for a way to continue this
triangle.*


The left border is said to be the "companion Pell sequence A099425", and
the right border is the factorials.

There is an explicit definition in terms of a missing sequence referred to
as "A118979" (different from the current A118979).

There are more clues involving A118981, which also need editing, (Richard
Mathar suggested a way to edit it in 2011, but I have not touched it
because I did not want to disturb the crime scene).

A118980 is a "cold case".  Richard Mathar worked on it in 2011, and I
struggled with it over the weekend.  Now I'm calling in "The Wolf" - the
combined minds of the Sequence Fans list. (The reference is to Pulp
Fiction.)