TITLE: If a polynomial has only real zeros then $a_{0}+a_{1}+\cdots+a_{n}\le\frac{(n+1)^n}{\binom{n}{s}(n-s)^{n-s}(s+1)^s}\cdot\max_{k}a_{k}$
QUESTION [7 upvotes]: Question:

For all real polynomials $P(x)=a_{0}+a_{1}x+\cdots+a_{n}x^n$ of degree $n$, with only real zeros,we have
  $$a_{0}+a_{1}+\cdots+a_{n}\le\dfrac{(n+1)^n}{\binom{n}{s}(n-s)^{n-s}(s+1)^s}\cdot\max_{k}a_{k},s=\lfloor \dfrac{n}{2}\rfloor$$


This problem is from Mitrinovic D.S Analytic inequalities (Springer 1970) Page 217.

He says that this inequality is due to L. Moser, J. R. Pounder and J.D. Dixon, who gave this generalization. 
But I can't find it. Can someone solve this?
Thank you!

REPLY [5 votes]: Since it seems the PDF linked by Macavity is not accessible to everyone, I reproduce it here :