The array begins:
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....|.n=1.|.n=2.|.n=3.|..n=4.|..n=5.|in OEIS.|
=============================================
k=3.|...6.|..10.|...15.|...21.|....253.|A113940
k=4.|...4.|...9.|...25.|...49.|....121.|A001248
k=5.|..35.|.247.|.1247.|..2501.|..4187.|A113941
k=6.|...6.|..15.|..703.|..1891.|..2701.|new
k=7.|.403.|.697.|.2059.|.25351.|.29539.|new
=============================================
|