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1978 IMO Longlists
2
2
Part of
1978 IMO Longlists
Problems
(1)
(x + 2x^2 +...+ nx^n)^2 = a_2x^2 + a_3x^3 +...+ a_{2n}x^{2n}
Source:
10/14/2010
If
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f(x) = (x + 2x^2 +\cdots+ nx^n)^2 = a_2x^2 + a_3x^3 + \cdots+ a_{2n}x^{2n},
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prove that
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12
a_{n+1} + a_{n+2} + \cdots + a_{2n} =\dbinom{n + 1}{2}\frac{5n^2 + 5n + 2}{12}
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algebra
generating functions
IMO Longlist 1978