Please Help

\((1+x+x^2+......+x^{14})^2\\~\\ =1+2x+3x^2+ .........+15x^{14}+14x^{13}+13x^{12}+............2x^{27}+x^{28}\)

 

 

 

so the product is:

 

\((1+x+x^2+x^3+.......x^{27})(1+2x+3x^2+ .........+15x^{14}+14x^{13}+13x^{12}+............2x^{27}+x^{28})\\ \)

 

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.