# Concatenating Pascal's Triangle

Calculus Level 5

Consider

the following sequence (A003590): $1, 11, 121, 1331, 14641, 15101051, 1615201561, \ldots$

where the $$n^\text{th}$$ term is the concatenation of all integers in the $$n^\text{th}$$ row of the Pascal's Triangle in that order, beginning with $$n=0$$.

Let $$L_n$$ be the number of digits in the $$n^\text{th}$$ term of this sequence.

Compute $$\displaystyle \lim_{n\to\infty}\exp\left(\frac{n^2}{L_n}\right)$$.

Notation: $$\exp(x)$$ denotes the exponential function, $$\exp(x) = e^x$$.

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