what is the circuit of 2^n -1

First could you clarify? Are you trying to get:

a) (2^n)-1

or

b) 2^(n-1)

I suspect it's a). If not let me know.

module pow_2toN(
    input          n,
    output        result
);
wire     shift_reg;
assign  shift_reg   = {16'd0,16'hffff} << n;
assign  result      = shift_reg;
endmodule

or...

module pow_2toN(
    input          n,
    output        result
);
genvar i;
generate
    for(i=0;i<16;i=i+1) begin : result_assigns
        assign result = (i < n) : 1'b1 : 1'b0;
    end
endgenerate
endmodule

or...

module pow_2toN(
    input          n,
    output  reg   result
);
integer i;
always @* begin
                    result      = 16'd0;
    for(i=0;i<16;i=i+1)
        if(i<n)     result   = 1'b1;
end
endmodule

or...

module pow_2toN(
    input          n,
    output  reg   result
);
integer i;
always @* begin
    result      = 16'd1;
    for(i=1;i<16;i=i+1)
        if(i<=n)    result      = {result,1'b0};
                    result      = result + 16'hffff;
end
endmodule

We could keep going but I digress. I may have some typos in there. What might be entertaining for you is to try all these variants and see what wildly different compilation results they produce.

Jake