editing
approved
T(2n,n) gives A340837.
(MAGMAMagma)
OEIS Server: https://oeis.org/edit/global/2944
proposed
Cf. A005649, A069321, A073146.
ColumnColumns k=0 gives-1 give: A000670, A232472.
Column k=0 gives A000670.
Row sums give A089677(n+1).
Cf. A005649, A069321, A073146, A089677 (row sums)..
Main diagonal gives A052841.