  In this note, among other results, we find the optimal constants of the
generalized Bohnenblust--Hille inequality for $m$-linear forms over
$\mathbb{R}$ and with multiple exponents $\left( 1,2,...,2\right) $, sometimes
called mixed $\left( \ell _{1},\ell _{2}\right) $-Littlewood inequality. We
show that these optimal constants are precisely $\left( \sqrt{2}\right) ^{m-1}$
and this is somewhat surprising since a series of recent papers have shown that
similar constants have a sublinear growth. This result answers a question
raised by Albuquerque \textit{et al.} in a paper published in 2014 in the
\textit{Journal of Functional Analysis}.
