Re: coefficients

On 14 Feb, 16:17, r...@xxxxxxxxxxxxxx (Rob Johnson) wrote:
In article <1171464223.131431.98...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

"Toxician" <fridgechemis...@xxxxxxxxx> wrote:
F(x)= (x^2+x^3+x^4+x^5)(x+x^2+....+x^7)(1+x+...+x^15)

What is the coefficient of x^15 ? I try to multiply all of them but it
becomes too long.

F(x) = x^3 + 3x^4 + 6x^5 + 10x^6 + 14x^7 + 18x^8 + 22x^9 + 25x^10
+ 27x^11 + 28x^12 + 28x^13 + 28x^14 + 28x^15 + 28x^16 + 28x^17
+ 28x^18 + 27x^19 + 25x^20 + 22x^21 + 18x^22 + 14x^23 + 10x^24
+ 6x^25 + 3x^26 + x^27

So the answer is 28.

Rob Johnson <r...@xxxxxxxxxxxxxx>
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Indeed, but since only x^15 is needed you could just look at
0+0+0+1+2+3+4+4+4+4+3+2+1+0+0+0 (and just slide left and right for
the other sums)

.

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