Calculate the number of Eulerian graphs on an n-dimensional hypercube.

A Eulerian graph is one in which each edge has a direction, and for
each vertex the number of edges directed "out of" this vertex is
equal to the number of edges directed "in to" it.

So by definition each vertex must have an even number of edges,
and thus "n" is required to be even.

It is known that for n=2 there are 2 such graphs, and for n=4 there
are 2970. It is additionally known that for n=6 the number lies
between 2.9 x 10^25 and 4.3 x 10^41 [1].

The aim is to calculate the value for n=6; for now, we assume n=8 is
out of reach.

[1] "Bounds on the Number of Eulerian Orientations" (A. Schrijver, 1983)
shows that the number of Eulerian orientations of a 2k-regular graph on
n vertices is between (2^{-k} (2k choose k))^n and sqrt((2k choose k)^n).