is it an egg cocoon from a praying mantis?
certainly looks like an egg/nest of some insect/spider.

Right! Specifically this is the egg case of a Chinese Preying Mantis. This mantis was accidentally introduced to the Western Hemisphere from the orient in the 1890’s first setting foot in Philadelphia USA. It is now quite common. The other common mantis is the Carolina Mantis which is the first one I ever set my eyes on when I was a boy. It was busy forming its own particular elongated egg case and to my young eyes it was quite a spectacle. The case pictured I noticed on a branch I had trimmed from a tree. I will fix it to a trellis in my garden.

Wow! I was looking at the front of my home and I found an egg case of a Carolina Mantis. Note that this egg case is not round, instead it is elongated in shape. As far as the difference in the adults, the Chinese mantis is brown as and adult whereas the Carolina mantis is green. When I added the photo of the Carolina mantis it wound up on top of the photos of the Chinese mantis.

I thought there was an extra photo this time.

they are amazing insects aren't they.

That's interesting but seems kinda early. Have you ever seen when the nymphs hatch out?

No Bath, not early at all. These cases are whipped up at this time of year with the eggs insulated inside. This is done right at this time before colder temperatures coming soon on the way impede the mantis’s metabolism. Next spring, with consistent warmer temperatures, the nymphs hatch from their egg case pouring out of it all attached from an seemingly single umbilical or rather bungee cord. They hang down from the egg case, break free, each go on their individual way. Some of these nymphs who don’t put enough distance between themselves will become their hatch mate’s first meal. As far as the mechanism of working their way out of the hard egg case, it seems that a proteolytic enzyme contained in the eggs is released when they burst upon hatching thus softening the case enough for the newly hatched nymphs to work their way out in mass. It is quite a sight and I am sure that someone has posted a video of this on YouTube or another venue. As far as the number of nymphs in a egg case that varies but certainly over a minimum of 50 to a max of about 200. The whole process occurs in about an hours time. They won’t hatch until warm weather has been consistent enough to provide small in size food sources such as aphids and midges. As I related before I raised these in my younger years and would feed them fruit flies ...which I also raised much to the annoyance of my mother. Looking back on this over 70 years ago it seems that I marched to the beat of a different drummer compared to what my twelve year old peers were interested in doing at that time:)

That's fascinating - worlds within worlds. I have seen the bungees dangle from my maple tree in Spring. They have free reign in my garden with always plenty to eat. I haven't seen a single aphid on my rose bushes. I think they are designed for the hunt/ambush with nearly 100% success.