n=1∑∞1⋅2⋅3+2⋅3⋅4+⋯+n(n+1)(n+2)n(n+2)
If the above expression is in the form BA where A and B are co-prime positive integers, then let ϕ=A×B.
φ=ϕϕ2ϕ3ϕ4⋯
Find the value of (5φ)!.
Notation:
! denotes the factorial notation. For example, 10!=1×2×3×⋯×10.
Inspired by Rohit Udaiwal.
Try the Part-2 here