If

Ω=ΣΣΣ(mn)/(m+n+p)!=5e/24

For the first summation
M=1 to +∞
Second summation
N=1 to +∞
Third summation
p=1 to +∞

I was giving a hint but still
ΣΣΣ(mn)/(m+n+p)!x^(m+n+p)=f(x)

Where f(0)=0

How can I show that

Ω=ΣΣΣ(mn)/(m+n+p)!=5e/24

Give the aformentioned hint