Let $\{m_n\}_{n=0}^{\infty}$ be a sequence of real numbers.

It is well known that there exist a positive Borel measure $\mu$ on the real line with moments given by $\{m_n\}_{n=0}^{\infty}$ if and only if the Hankel matrix
\begin{align}
A=(m_{i+j})_{i,j=0}^\infty,
\end{align}

is positive semi-definite.

In general the condition above condition can be difficult to verify.

My question: Is there a 'simpler' sufficient condition that can be checked?

Thanks.