square arrangements with bit-wise constraints

[Max A.]

There is a problem at MathPages about arrangements of numbers
0,1,...,15 into 4x4 array with certain bit-wise constraints:
http://www.mathpages.com/home/kmath352.htm

This problem (and its variants) can be easily generalized to
(2^n)x(2^n) arrays, e.g.:

In how many distinct ways can the integers 0 through 2^(2n)-1 be arranged
in a (2^n)x(2^n) array such that the bit-wise OR over each row, each column,
and each diagonal is 2^(2n)-1, and the bit-wise AND over each row, column,
and diagonal is 0?

Does anybody wish to compute corresponding sequences and submit them to OEIS?

Regards,
Max