Pyramid #186
Generating function
$$U_{186}(x, y) = \frac{- x + \sqrt{x^{2} + 2 x + 4 y + 1} - 1}{2 y}$$
Explicit formula
$$T_{186}(n, m, k) = \frac{\left(-1\right)^{- m + n} k {\binom{k + m + n - 1}{n}} {\binom{k + 2 m + n - 1}{m}}}{k + m}$$
Data table
1 -1 2 -5 14 -42 132
-1 3 -10 35 -126 462 -1716
1 -6 3 -140 630 -2772 12012
-1 1 -7 42 -2310 12012 -60060
1 -15 14 -105 693 -42042 240240
-1 21 -252 231 -18018 126126 -816816
1 -28 42 -462 42042 -336336 2450448
Export
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