We still can't say for sure, but I can say that it hasn't grown from the tree stump.
I'm still with Rodgersia aesculifolia, if it had grown from a conker it wouldn't have got so big in a season and if it had started to grow last year we would be seeing the bottom part of the stem hardened. There doesn't appear to be anything growing there in November 2015.
Unless there are Aesculus which can grow that quickly! Mine don't, they are slow from a conker.
You won't be able to root such a stem. You might be able to carefully dig up the plant which is there but that's risky, someone might have planted them there and it would belong to the local council.
