Product_{k=1..n} x^k*(1-x^k)
n=1 x - x^2
n=2 x^3 - x^4 - x^5 + x^6
n=3 x^6 - x^7 - x^8 + x^10 + x^11 - x^12
Integral Product_{k=1..n} x^k*(1-x^k) dx
n=1 x^2/2 - x^3/3
n=2 x^4/4 - x^5/5 - x^6/6 + x^7/7
n=3 x^7/7 - x^8/8 - x^9/9 + x^11/11 + x^12/12 - x^13/13
For Integral_{x=0..1} set x=1
n=1 1/2 - 1/3 = 1/6, a(1)=6
n=2 1/4 - 1/5 - 1/6 + 1/7 = 11/420, a(2)=420
n=3 1/7 - 1/8 - 1/9 + 1/11 + 1/12 - 1/13 = 293/72072, a(3)=72072
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