Number of labelings of symmetric hexagonal tilings

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I am searching for the Number of labelings of symmetric hexagonal tilings

If the hexagon is of the form P(n,n,n) then the coefficients can be found here A217311

I am looking for the coefficients of P(4,2,4)

After doing some research I found P(2,3,2),P(3,3,4),P(3,4,4)... and some others but not the one I am looking for

enter image description here

I took the img from https://arxiv.org/pdf/cond-mat/0004145.pdf

mathworld states that enter image description here

http://mathworld.wolfram.com/PlanePartition.html

Using the above formula I can only calculate the first term which is 1764.

How can i find the other terms?

can anybody help me find the coefficients for P(4,2,4)?

thanx