Pyramid #902
Generating function
$$U_{902}(x, y) = x \left(1 - y\right) + \frac{\sqrt{4 x + \frac{1}{\left(1 - y\right)^{4}}}}{2 \left(1 - y\right)} + \frac{1}{2 \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{902}(n, m, k) = \begin{cases}{\binom{3 k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}} {\binom{3 k + m - 4 n - 1}{m}}}{n} \end{cases} $$
Data table
1 3 6 1 15 21 28
2 -2 0 0 0 0 0
-1 5 -1 1 -5 1 0
2 -18 72 -168 252 -252 168
-5 65 -39 143 -3575 6435 -858
14 -238 1904 -952 3332 -86632 173264
-42 882 -882 5586 -25137 854658 -2279088
Export
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