Strange sum

Calculus Level 3

If

112+4+122+8+132+12+=pq, \frac{ 1 }{ 1^2 + 4 } + \frac{ 1}{2^2 + 8 } + \frac{ 1 }{ 3^2 + 12 } + \ldots = \frac { p}{q},

where pp and qq are coprime positive integers, what is p+q p + q ?

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