(1+x+x2+......+x14)2 =1+2x+3x2+.........+15x14+14x13+13x12+............2x27+x28
so the product is:
(1+x+x2+x3+.......x27)(1+2x+3x2+.........+15x14+14x13+13x12+............2x27+x28)
I am interested in the sum of the x^28 coefficients.
This is it
2+3+....+14+15 +14+13+......+2+1
=2(2+3+4+5+6+7+8+9+10+11+12+13+14)+15 +1
= 224
So the coefficient of x^28= 224
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Maybe BaldisBasics knows a short cut but he certainly has not explained it to me.