what is the circuit of 2^n -1

if it is just that simple you could write

module MyPower ( clk , In_N , Out_P );

input clk;

input [ 3:0] In_N;

output [15:0] Out_P;

reg [15:0] Out_P;

always @ ( posedge clk )

case ( In_N )

4'd0 : Out_P <= 16'd1;

4'd1 : Out_P <= 16'd2;

4'd2 : Out_P <= 16'd4;

4'd3 : Out_P <= 16'd8;

4'd4 : Out_P <= 16'd16;

4'd5 : Out_P <= 16'd32;

4'd6 : Out_P <= 16'd64;

4'd7 : Out_P <= 16'd128;

4'd8 : Out_P <= 16'd256;

4'd9 : Out_P <= 16'd512;

4'd10 : Out_P <= 16'd1024;

4'd11 : Out_P <= 16'd2048;

4'd12 : Out_P <= 16'd4096;

4'd13 : Out_P <= 16'd8192;

4'd14 : Out_P <= 16'd16384;

4'd15 : Out_P <= 16'd32768;

endcase

endmodule

but you could try to implement some kind of shift functionality