Summing The Series

Algebra Level 4

4×3×2×13!+2!+1!\dfrac{4\times{3}\times{2}\times{1}}{3!+2!+1!}+5×4×3×24!+3!+2!\dfrac{5\times{4}\times{3}\times{2}}{4!+3!+2!}+.......+2015×2014×2013×20122014!+2013!+2012!\dfrac{2015\times{2014}\times{2013}\times{2012}}{2014!+2013!+2012!}= aa

Find a\lfloor{a}\rfloor

...\lfloor...\rfloor is the greatest integer less than equal to [......]

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