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Question: expanding fractions into polynomial

Question:expanding fractions into polynomial

Sini 10 Maple
February 24 2011
0

Hi,

I am trying to expand the following into a polynomial on maple:


1/((1+x)*(1+x^2)*(1+x^3)*(1+x^4)*(1+x^5)*(1+x^6)*(1+x^7)*(1+x^8)*(1+x^9)*(1+x^10))

to get  1 + x + 2 x^(2)+ 3 x^(3)+ 5 x^(4)+ 7 x^(5)+ 11 x^(6)+ 15 x^(7)+ 22 x^(8)+ 30 x^(9)+ 42 x^(10)...  

I tried to use the expand() code but it still would not expand it to the above polynomial...

is there any other way to get to this polynomial from that fraction please?

Any help will be appreciated

Many Thanks
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