When you want to get the square of a binomial of two variables x and y, you will have:

`$(x+y)^2 = x^2 + 2xy + y ^2$`

And the cube:

`$(x+y)^3 = x^3 + 3x^2y + 3xy^2 +y^3$`

It is known from many centuries ago that for an exponent n, the result of a binomial x + y raised to the n-th power is:

Or using the sumation notation:

Each coefficient of a term has the following value:

Each coefficient value coincides with the amount of combinations without replacements of a set of n elements using only k different ones of that set.

Let's see the total sum of the coefficients of the different powers for the binomial:

`$(x+y)^0(1)$`

`$(x+y)^1 = x+y(2)$`

`$(x+y)^2 = x^2 + 2xy + y ^2(4)$`

`$(x+y)^3 = x^3 + 3x^2y + 3xy^2 +y^3(8)$`

We need a function that may generate an array with the values of all the coefficients sums from 0 to the value of n included and has the addition of all the sum values as last element.

We add some examples below:
``` 
f(0) = [1, 1]
f(1) = [1, 2, 3]
f(2) = [1, 2, 4, 7]
f(3) = [1, 2, 4, 8, 15]
``` 

Features of the test
``` 
Low Performance Tests
Number of tests = 50
9 < n < 101

High Performance Tests
Number of Tests = 50
99 < n < 5001
```

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def f(n):\n    x=[2**i for i in range(n+1)]\n    x.append(2**(n+1)-1)\n    return x'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'f'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5494