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COMMENTS
| The column sequences can also be calculated using sequences which map to associated partitions. For example, 4 32 132 392 ... maps to 5+5+5+4 (n=19) and sequence 5 50 245 840 ... maps to 4+4+4+4+3. Many partitions map to the same sequences since the mapping depends only on the "degree" of the partition. In the above two cases, the degrees are 31 and 41 respectively. At n = 20 the relevant degrees are: 21,31,211,311,22,221,42,212,321,24 and 61. The associated partitions can be permuted with the number of ways as indicated: 3 4 12 20 6 30 15 30 60 15 and 7 ways. Adding these values with the 32 and 50 ways from our first two sequences confirms that A110553(2) = 284.
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