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Calculus Level 5

\[ \large \displaystyle\sum _{ n=1 }^{ \infty }{ \dfrac { { H }_{ n }-\ln { n } -\gamma }{ n } } =-\dfrac { { \gamma }^{ t } }{ a } -h{ \gamma }_{ i }+\dfrac { { \pi }^{ n } }{ { i }_{ 1 } } \]

The equation above holds true for positive integers \(t,a,h,i, n\) and \(i_1\). Find \(t+a+h+i+n+i_1\).

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