# Domino Sums Take 2

A single domino is a rectangular tile divided into two square ends marked with spots. A domino set of order $$n$$ consists of all the domino tile combinations with spot counts from $$0$$ to $$n$$ inclusive.

$$T(n)$$ is the sum of the totals of the two spot counts on each tile in the domino set of order $$n$$, and $$P(n)$$ is the sum of the products of the two spot counts on each tile in the domino set of order $$n$$.

For example, a domino set of order $$2$$ would consist of the domino tiles with numbers $$(0, 0)$$, $$(0, 1)$$, $$(0, 2)$$, $$(1, 1)$$, $$(1, 2)$$, $$(2, 2)$$, such that \begin{align} T(2) &= (0 + 0) + (0 + 1) + (0 + 2) + (1 + 1) + (1 + 2) + (2 + 2) \\&= 12\\\\ P(2) &= (0 \cdot 0) + (0 \cdot 1) + (0 \cdot 2) + (1 \cdot 1) + (1 \cdot 2) + (2 \cdot 2) \\&= 7. \end{align} What is $${\displaystyle \lim_{n\to\infty}} \frac{n T(n)}{P(n)}?$$

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