Infinite Factorial Summation with a twist - Part 2

Calculus Level 4

21!+122!+283!+504!+785!+\large \dfrac{2}{1!} + \dfrac{12}{2!} + \dfrac{28}{3!} + \dfrac{50}{4!} + \dfrac{78}{5!} + \ldots

If the value of the above summation be equal to A+BeA + Be for positive integers AA and BB, find the value of A+BA+B.

Clarification: The numbers in the numerators follows a quadratic polynomial.

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