[seqfan] Chunk & Sum / Wooden arrangements

[Éric Angelini]

Hello SeqFans,
After quite a mess on Math-Fun due to my lazy old brain,
please find here the first 14 terms of the Chunk & Sum 
sequence computed by the talented Frank Stevenson:
S = 1, 21, 33, 325, 564, 687, 7489, 9090, 10359, 107101, 912081, 1288716, 13123324, 141300915,…
As I don't want to repeat the same mess on the OEIS,
could someone write a good definition for this seq?
And submit it to Neil's database (if interesting)?
Computing more terms would be great too -- but the 
size of the "wooden arrangements" for n > 14 is scary
(see below). More explanations here on my blog -- after
rephrasing a lot: https://bit.ly/32TAoKn
Best,
É.
P.-S. 
I realize that the seq of "wooden arrangements" could
be entered in the OEIS too, perhaps. We would then have
those 14 terms to start, the last one being 19-digit long:

T = 1, 21, 132, 4321, 43521, 154632, 6517432, 76518432, 768519432, 98471106532, 1651142910873, 411129101287653, 97864125313121110, 4211113109141287653,...