Generating function
$$U_{1456}(x, y) = \frac{\left(1 - y\right)^{2} \left(- \frac{2 x}{\left(1 - y\right)^{2}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{2}} + 1} + 1\right)}{2 x^{2}}$$
Explicit formula
$$T_{1456}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{2 k + m + 2 n - 1}{m}}}{k + n}$$
Data table
1 2 3 4 5 6 7
2 8 2 4 7 112 168
5 3 105 28 63 126 231
14 112 504 168 462 11088 24024
42 42 231 924 3003 84084 21021
132 1584 10296 48048 18018 576576 1633632
429 6006 45045 24024 102102 3675672 11639628
Export
expand_less