What's with that weird fraction?

Algebra Level 3

Let a1,a2,a3,a4a_1,a_2,a_3,a_4 be positive real numbers such that

a1+a2+a3+a4=52.a_1+a_2+a_3+a_4=52.

Let the maximum possible value of a1a2a3a4a_1a_2a_3a_4 be PP.

Given that Pn(mod7)P\equiv n\pmod7, find the value of n3+n2n+121\frac{n^3+n^2-n+1}{2}-1.

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