Pyramid #187
Generating function
$$U_{187}(x, y) = \frac{- y + \sqrt{4 x + y^{2} + 2 y + 1} - 1}{2 x}$$
Explicit formula
$$T_{187}(n, m, k) = \frac{\left(-1\right)^{- m + n} k {\binom{k + 2 n - 1}{n}} {\binom{k + m + 2 n - 1}{m}}}{k + n}$$
Data table
1 -1 1 -1 1 -1 1
-1 3 -6 10 -15 21 -28
2 -1 3 -70 140 -252 420
-5 35 -14 42 -1050 2310 -4620
14 -126 63 -231 693 -18018 42042
-42 462 -2772 12012 -42042 126126 -336336
132 -1716 12012 -6006 24024 -816816 2450448
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