[seqfan] towards a new series for e

[Jaume Oliver i Lafont]

Hello,

e~=H_8(1-1/80^2) is equation (9) in
http://mathworld.wolfram.com/eApproximations.html

There might be a simple series whose first two terms yield this approximation,
but i have failed several times to find it.

Can you do it? At least next term inside the parenthesis?

Jaume