Given Wikipedia's discussion of Double Factorials, can anyone suggest where I might find a bignum version of this for Perl, or else suggest how it might be written?
Perl will handle whatever your C compiler can handle, for anything bigger you should be using Math::BigInt.
I would recommend you read perlnumber.
A definition for the double factorial (in perl golf):
sub f{$_[0]&&$_[0]>=2?$_[0]*f($_[0]-2):1}