Pyramid 1202

Pyramid #1201

Pyramid #1202

Pyramid #1203

Generating function

$$U_{1202}(x, y) = \frac{\left(- 2 x \left(y + 1\right)^{2} - \sqrt{- 4 x \left(y + 1\right)^{2} + 1} + 1\right)^{3}}{8 x^{6} \left(y + 1\right)^{12}}$$

Explicit formula

$$T_{1202}(n, m, k) = \frac{3 k {\binom{2 n}{m}} {\binom{6 k + 2 n}{n}}}{3 k + n}$$

Data table
1	0	0	0	0	0	0
6	12	6	0	0	0	0
27	108	162	108	27	0	0
11	66	165	22	165	66	11
429	3432	12012	24024	3003	24024	12012
1638	1638	7371	19656	34398	412776	34398
6188	74256	408408	136136	306306	4900896	5717712

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