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The result appears to be the square of an integer, but I don't know why.

n(n+1)(n+2)(n+3) n4+6n3+11n2+6n. If n 1 then the sum is 24 and adding 1 yields 25 or 52. If n 2. them the sum is 120 and adding 1 yields 121 or 112. If n 5 the sum is 1680 and adding 1 yields 1681 or 412.

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