\[\large \sum _{ n=1 }^{ \infty }{ \dfrac { { n }^{ 4} }{ { 4 }^{ n }\cdot n! } } =\dfrac { c~\sqrt [ a ]{ e } ~\pi^{d-1}}{ b } \]

If the equation above holds true for positive integers \(a,b,c,d\), with \(b, c\) coprime, find \(a+b+c+d\).

**Clarification**: \(e \approx 2.71828\) denotes the Euler's number.

Try part-1 here.

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