Sumtegrals! - 2

Calculus Level 4

\( K = \displaystyle\sum_{n=0}^{\infty} \frac{9^n}{(n+3)(n+2)n!} \)

If the infinite sum above can be expressed in the form \( \frac{1}{a} (ce^b + d) \), find the value of \( a + b + c + d + 1\)

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