You can dry store the seeds in the refrigerator in a tightly closed container for some time, but I think the fresher the seed, the faster it will germinate.
Much has been written on Arisaema-L and other lists about germinating Arisaema seed, with many elaborate methods described. I have found seeds easy to germinate, requiring no cold scarification. I've even had old seed, stored in the refrigerator for several years, germinate readily. I soak dry seeds in water with a drop of dishwashing liquid for a couple of days to a week, changing the water daily and sow in a soiless medium, covering the seed with granite grit.
Depending on your bagged medium, you may want to add grit, perlite or coarse sand so that it drains very sharply.
Germination for some starts in a month or so, either at room temperature or on my cool greenhouse bench. Others take longer, but all I have tried seem to germinate within a few months. Some species, such as A. elephas and A. lobatum do not produce a leaf above ground the first season, so don't throw out any seedpots for lack of activity until you've held them for at least two full years. I always sift through pots before dumping them, just in case.
The trick (for me, at least) is not getting seeds to germinate, but keeping seedlings and baby tubers alive long enough for them to get large enough to plant out in the garden. I have lost quite a few seedlings to rotting tubers due to the peat based medium staying too wet. It's a delicate balance once the seedlings enter their first dormancy. They don't want to get bone dry, but if they are kept too wet, they rot. This is especially a problem with A. sikokianum, who really resents wet when dormant.
I seem to have better luck if I get busy and repot the baby tubers as soon as they go dormant, using my normal potting mix (compost, leaf mold, pine bark fines and granite grit), which doesn't seem to disintegrate into a wet, mucky mess like peat based mediums do.
