closed form of the generating function

any one can get a closed form of the generating function of the sequence [MATH]a_n[/MATH]

[MATH]a_n=n\left((-1)^n\left(1-n\right)+3^{n-1}\right)[/MATH]

you can refer websites Generating function - Wikipedia, the free encyclopedia
Generating Function -- from Wolfram MathWorld


it might be helpful.

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