A weird Series

Algebra Level 3

Sn=1+94+369+10016+22525+44136++(1+2++n)2n2{S_{n}=1+\dfrac{9}{4}+\dfrac{36}{9}+\dfrac{100}{16}+\dfrac{225}{25}+\dfrac{441}{36} +\ldots + \frac{(1+2+\ldots+n)^2}{n^2} }

Evaluate S16\large{S_{16}}.

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