# Pascal's hockey shot

$\begin{array}{c} 1 \end{array} \\ \begin{array}{cc} 1 & 1 \end{array} \\ \begin{array}{ccc} 1 & 2 & \color{red}{1}\end{array} \\ \begin{array}{cccc} 1 & 3 & \color{red}{3} & 1\end{array} \\ \begin{array}{ccccc} 1 & 4 & \color{red}{6} & 4 & 1\end{array} \\ \begin{array}{cccccc} \vdots & \hphantom{\vdots} & \vdots & \hphantom{\vdots} & \vdots \end{array}\\ \begin{array}{cccccc} 1 & 25 & \color{red}{300} & 2300 & 12650 & \cdots \end{array} \\ \begin{array}{ccccccc} 1 & 26 & 325 & 2600 & 14950 & \cdots & \hphantom{1000} \end{array} \\$

Pascal's Triangle is shown above for the $$0^\text{th}$$ row through the $$4^\text{th}$$ row, and part of the $$25^\text{th}$$ and $$26^\text{th}$$ rows are also shown above.

What is the sum of all the $$2^\text{nd}$$ elements of each row up to the $$25^\text{th}$$ row?

Note: The visible elements to be summed are highlighted in red.

Additional clarification: The topmost row in Pascal's Triangle is the $$0^\text{th}$$ row. Then, the next row down is the $$1^\text{st}$$ row, and so on. The leftmost element in each row of Pascal's Triangle is the $$0^\text{th}$$ element. Then, the element to the right of that is the $$1^\text{st}$$ element in that row, and so on.

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