Generating function
$$U_{1195}(x, y) = \frac{4 y^{4} \left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)}{y} - \sqrt{- \frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1} + 1\right)^{2}}{x^{4} \left(1 - \sqrt{1 - 4 y}\right)^{4}}$$
Explicit formula
$$T_{1195}(n, m, k) = \frac{2 k n {\binom{4 k + 2 n}{n}} {\binom{2 m + n - 1}{m}}}{\left(2 k + n\right) \left(m + n\right)}$$
Data table
nan 0 0 0 0 0 0
4 4 8 2 56 168 528
14 28 7 196 588 1848 6006
48 144 432 1344 432 14256 48048
165 66 231 792 27225 9438 33033
572 286 1144 429 1573 572572 208208
2002 12012 54054 22022 858858 3279276 12388376
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