This is the 6th row of the array from Aldosray and Stewart:
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Nodes.|.valency.............................................................
=====.|.v=1.|....v=2.|......v=3.|........v=4.|..........v=5.|............v=6
1.....|..1..|......1.|........1.|..........1.|............1.|..............1
2.....|..2..|......5.|........9.|.........14.|...........20.|.............27
3.....|..4..|.....38.|......170.|........575.|.........1561.|...........3696
4.....|..9..|....416.|.....6690.|......62725.|.......410438.|........2076725
5.....|.20..|...6209.|...436277.|...14000798.|....264632734.|.....3403484793
6.....|.51..|.117020.|.42722972.|.5554560632.|.355631996061.|.13505066262007
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