[seqfan] It appears that I have stumbled upon new (?) identity (?) involving Pi and sqrt(3)

[Alexander P-sky]

Hi,

It appears that I have stumbled upon new (?)  identity (?) involving
Pi and sqrt(3)

sum(1/(n!/floor(n/2)!^2),n=0...infinity) = 4/3 + 8*Pi/(9*sqrt(3))

Both left and right sides give something like
2.94559943487486031163918067345969398425250333163799162272878660923388727211231456327477776729960903898331

I am using at the moment WolframAlpha Pro (just for two weeks of free
evaluation)
It (WolframAlpha Pro) times out on me in proving or disproving
whether this identity is true or false.

Could some one check it out, please ?

Thanks,
Best Regards,
Alexander R. Povolotsky