Pyramid 89

Pyramid #88

Pyramid #89

Pyramid #90

Generating function

$$U_{89}(x, y) = \frac{1}{2} - \frac{\sqrt{- 4 x - 4 y + 1}}{2}$$

Explicit formula

$$T_{89}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{k {\binom{m + n}{m}} {\binom{- k + 2 m + 2 n - 1}{- k + m + n}}}{m + n} \end{cases} $$

Data table
1	1	1	2	5	14	42
1	2	6	2	7	252	924
1	6	3	14	63	2772	12012
2	2	14	84	462	24024	12012
5	7	63	462	3003	18018	102102
14	252	2772	24024	18018	1225224	7759752
42	924	12012	12012	102102	7759752	54318264

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