What is the acceleration for the expansion of the Universe? I've found that the speed of expansion is about $70\frac{km}{s\cdot 10^{6}pc}$.

But what is the acceleration of expansion in terms of $\frac{km}{s^{2}\cdot 10^{6}pc}$ ?

I want to know how fast this value of "70" is changing, ie what is $\mathrm{d}H_0/\mathrm{d}t$?
The figure below shows the evolution of the Hubble parameter $H$ from 10 billion years (Gyr) ago, to 10 Gyr into the future:



As you can see, the change in $H$ is modest nowadays, compared to the past. The "acceleration" of the expansion at any point in time is given by the tangent to the curve at that time. Today, the change is $dH/dt \simeq -1.2\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}\,\mathrm{Gyr}^{-1}$, or roughly $-10^{-17}\,\mathrm{km}\,\mathrm{s}^{-2}\,\mathrm{Mpc}^{-1}$.

In other words, it will take roughly a billion years before the expansion rate has decreased by $1\,\mathrm{km}\,\mathrm{s}^{-1}$, and it asymptotically approaches some $57\,\mathrm{km}\,\mathrm{s}^{-1}$.

Since $H$ is defined as $(da/dt)\,/\,a$, where $a$ is the scale factor (the "size" of the Universe), a constant $H$ implies that $a\propto e^{Ht}$; that is, the size of the Universe increases exponentially.