4, 3, 2, 1: Part 2

Calculus Level 4

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

If the equation above holds true for positive integers, find $a+b$ .

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