Question: Want to write an expression in sigma notation

Dear Users!

Hope you would be fine. I want to write an expression in sigma notation which control ny n (any constant >0);
for n =1 expression expand as

E[1]+1

for n =2 expression expand as
E[1]*E[2]*a[12]+E[1]+E[2]+1;

for n =3 expression expand as

E[1]*E[2]*E[3]*a[123]+E[1]*E[2]*a[12]+E[1]*E[3]*a[13]+E[2]*E[3]*a[23]+E[1]+E[2]+E[3]+1;

for n =4 expression expand as

E[1]*E[2]*E[3]*E[4]*c[1234]+E[1]*E[2]*E[3]*a[123]+E[1]*E[2]*E[4]*a[124]+E[1]*E[3]*E[4]*a[134]+E[2]*E[3]*E[4]*a[234]+E[1]*E[2]*a[12]+E[1]*E[3]*a[13]+E[1]*E[4]*a[14]+E[2]*E[3]*a[23]+E[2]*E[4]*a[24]+E[3]*E[4]*a[34]+E[1]+E[2]+E[3]+E[4]+1;

and so on.

I am waiting your kind respons. Thanks

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