Infinite Natural Logarithmic Factorial Summation

Calculus Level 4

1+31!ln3+1+322!(ln3)2+1+333!(ln3)3+\large \dfrac{1+3}{1!}\ln3 + \dfrac{1+3^2}{2!}(\ln3)^2 + \dfrac{1+3^3}{3!}(\ln3)^3 + \ldots

What is the value of the above expression?

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