Pyramid 1313

Pyramid #1312

Pyramid #1313

Pyramid #1314

Generating function

$$U_{1313}(x, y) = \frac{\left(- 2 x \left(y + 1\right)^{2} - \sqrt{- 4 x \left(y + 1\right)^{2} + 1} + 1\right)^{3}}{8 x^{6} \left(y + 1\right)^{10}}$$

Explicit formula

$$T_{1313}(n, m, k) = \frac{3 k {\binom{2 k + 2 n}{m}} {\binom{6 k + 2 n}{n}}}{3 k + n}$$

Data table
1	2	1	0	0	0	0
6	24	36	24	6	0	0
27	162	405	54	405	162	27
11	88	308	616	77	616	308
429	429	19305	5148	9009	108108	9009
1638	19656	108108	36036	81081	1297296	1513512
6188	86632	563108	2252432	6194188	12388376	18582564

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