Tensor dot product with rank one tensor from vector

I'm trying to compute an inner product between tensors in numpy.

I have a vector $x$ of shape (n,) and a tensor $y$ of shape d*(n,) with d 1 and would like to compute $\langle y, x^{\otimes d} \rangle$. That is, I want to compute the sum

$$\langle y, x^{\otimes d} \rangle= \sum_{i_1,\dots,i_d\in\{1,\dots,n\}}y[i_1, \dots, i_d]x[i_1]\dots x[i_d].$$

A working implementation I have uses a function to first compute $x^{\otimes d}$ and then uses np.tensordot:

def d_fold_tensor_product(x, d) - np.ndarray:
    
    Compute d-fold tensor product of a vector.
    
    assert d  1, Tensor order must be bigger than 1.

    xd = np.tensordot(x, x, axes=0)
    for _ in range(d-2):
        xd = np.tensordot(xd, x, axes=0)

    return xd

n = 10
d = 4
x = np.random.random(n)
y = np.random.random(d * (n,))
result = np.tensordot(y, d_fold_tensor_product(x, d), axes=d)

Is there a more efficient and pythonic way? Perhaps without having to compute $x^{\otimes d}$.