Pensieve header: Enable the likes of Table[As[n,6], As[k,0,n], Binomial[n,k]].

SetAttributes[As,HoldAll];
As /: (op:Do|Product|Sum|Table)[As[iter___], ℰ__] := op[ℰ, {iter}]

p=1;Do[As[k,1,5], p*=k]; p

Product[As[k,1,7], k]

Sum[As[k,1,100], k]

Table[As[n,6], As[k,0,n], Binomial[n,k]]