Consider $N+1$ unformly spaced distinct points $$ -1 = x_0 < x_1 < \ldots < x_N = 1.0 $$ Their Vandermonde matrix is $$ \begin{bmatrix} 1 & x_0 & x_0^2 & \ldots & x_0^N \\ 1 & x_1 & x_1^2 & \ldots & x_1^N \\ \vdots & \vdots & \vdots & & \vdots\\ 1 & x_N & x_N^2 & \ldots & x_N^N \end{bmatrix} $$ We will use the cond function from numpy.linalg to compute the condition number. By default, it uses the 2-norm.
from numpy import linspace,zeros
from numpy.linalg import cond
for N in range(1,30):
x = linspace(-1.0,+1.0,N+1)
V = zeros((N+1,N+1))
for j in range(0,N+1):
V[j][:] = x**j # This is transpose of V as defined above.
print("%8d %20.8e" % (N,cond(V.T)))
1 1.00000000e+00 2 3.22550493e+00 3 8.01156105e+00 4 2.35309087e+01 5 6.38272826e+01 6 1.89814113e+02 7 5.35353118e+02 8 1.60544370e+03 9 4.62644992e+03 10 1.39516269e+04 11 4.07548818e+04 12 1.23389738e+05 13 3.63830758e+05 14 1.10480853e+06 15 3.28003166e+06 16 9.98312389e+06 17 2.97935974e+07 18 9.08473096e+07 19 2.72240824e+08 20 8.31377050e+08 21 2.49966299e+09 22 7.64316645e+09 23 2.30433941e+10 24 7.05345370e+10 25 2.13143827e+11 26 6.53020161e+11 27 1.97722392e+12 28 6.06236493e+12 29 1.83901872e+13
As $N$ increases, the condition number of the Vandermonde matrix is increasing, and the condition number is quite large for even moderate values of $N$ like $N=30$.