# 300 Followers Problem - Combinatorial Expressions!

$\large{R_n = \sum_{k=0}^{n} \binom{2k}{k} \quad , \quad S_n = \sum_{k=0}^{n} (-1)^k \binom{2k}{k} }$

For $$n$$ belonging to the set of non-negative integers, define $$R_n$$ and $$S_n$$ as of above. Also define $$A_n$$ and $$B_n$$ as:

• $$\large{A_n = \displaystyle R_n^2 + 2 \sum_{k=1}^n \binom{2n+2k}{n+k}R_{n-k} }$$

• $$\large{B_n = \displaystyle S_n^2 + 2 \sum_{k=1}^n (-1)^{n+k} \binom{2n+2k}{n+k}S_{n-k} }$$

Evaluate the value of: $$\large{\log_2\left(5B_{2015} - 3A_{2015} \right) }$$ upto three correct places of decimals.

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