ok, so the 2^N terms are each a product of N terms,
a[i][j], where j can be 0 or 1 and i goes from 0 to N1
ie, each one looks like, say
a[0][0] * a[1][0] * a[2][1] * a[3][0] * ... * a[N1][1]
So, we want do some binary magic.
how about something like:
#!/usr/bin/perl wl
use strict;
use Data::Dumper;
my $N = 4;
my $size = 32;
my $arr = [[1, 2],
[3, 4],
[5, 6],
[7, 8]];
my @C;
foreach my $m (0..2**$N  1) {
my $vec = "";
vec($vec, 0, $size) = $m;
my @bits = split(//, unpack("B*", $vec));
splice(@bits, 0, $size  $N);
# so @bits now contains the binary expansion of $m
# with exactly $N bits, as you can verify by uncommenting
# print join "::", @bits;
$C[ $m ] = 1;
# now we multiply the $N terms $arr>[i][j]
# where j is the ith bit in the binary expansion of $m
$C[ $m ] *= $arr>[ $_ ][ $bits[$_] ] for 0..$N1;
}
print Dumper \@C;
note, $size must be a power of 2, for vec to work, and unless you're on a 64bit machine, it probably cannot be more than 32.
also, this works for $N no more than 31(32?)  but you may have other problems (memory say), if you want to go above that.
Hope this helps.

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