# Coefficients of symmetric polynomials

Hi everyone,

I want to get the coefficients of symmetric polynomials, and then make them a vector. I tried the following code:

```
Sym = SymmetricFunctions(QQ)
e = Sym.elementary()
g = e[2, 1] - 3*e[3]
g.coefficients()
```

The output is `[1, -3]`

, but my desired result is `[0, 1, -3]`

, where the zero is the coefficient of `e[1, 1, 1]`

.
I found this question get the coefficients from the polynomial, but it seems `.coefficients(sparse=False)`

and `.list()`

only work for the univariate polynomial ring.
Thank you in advance for your answer and comments!

Edit:
I would like to make some clarification about the desired result. What I want is a vector of dimension `p(n)`

where `p`

is the partition function. And each of its components is the coefficient of `g`

under the basis `e(part)`

, where `part`

ranges over all the partitions of `n`

.