Pyramid #1444
Pyramid #1445
Pyramid #1446
Generating function
$$U_{1445}(x, y) = \frac{y + 1}{\left(- x \left(y + 1\right)^{3} + 1\right)^{3}}$$
Explicit formula
$$T_{1445}(n, m, k) = {\binom{k + 3 n}{m}} {\binom{3 k + n - 1}{n}}$$
Data table
1 1 0 0 0 0 0
3 12 18 12 3 0 0
6 42 126 21 21 126 42
1 1 45 12 21 252 21
15 195 117 429 10725 19305 2574
21 336 252 1176 3822 91728 168168
28 532 4788 27132 108528 325584 759696
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