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        riddles >> medium >> Recursive Polynomial
        
(Message started by: Ronno on Apr 8^th, 2010, 9:10pm)

Title: Recursive Polynomial
Post by Ronno on Apr 8^th, 2010, 9:10pm

Define a sequence <x_n> by:
x_1=1
x_2=x
x_(n+2)=x*x_(n+1)+n*x_n for n>=3
Let P_n(x)=x_(n-1)*x_(n+1)-(x_n)^2 for n>=2
Prove or disprove that the coefficients of P_n(x) are all non-negative, except for the constant term when n is odd.