4, 3, 2, 1: Part 2

Calculus Level 3

\[\large \sum _{ n=1 }^{ \infty }{ \dfrac { { n }^{ 2 } }{ 4\cdot { 3 }^{ n }\cdot n! } } =\dfrac { \sqrt [ a ]{ e } }{ b } \]

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

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

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