#Python 3, 201 184 bytes

def f(n):x,z,m=[1],[0],n-1;l=[z*m+x+z*m];exec("x=[*map(sum,zip(z+x,x+z))];l.append(z*(n-len(x))+[b for a in zip(x,z*len(x))for b in a][:-1]+z*(n-len(x)));"*m);return[*map(sum,zip(*l))] 

Python 3, 201 184 bytes

def f(n):x,z,m=[1],[0],n-1;l=[z*m+x+z*m];exec("x=[*map(sum,zip(z+x,x+z))];l.append(z*(n-len(x))+[b for a in zip(x,z*len(x))for b in a][:-1]+z*(n-len(x)));"*m);return[*map(sum,zip(*l))] 

#Python 3, 201 bytes

def f(n):x,l=[1],[[0]*(n-1)+[1]+[0]*(n-1)];exec("x=[*map(sum,zip([0]+x,x+[0]))];l.append([0]*(n-len(x))+[b for a in zip(x,[0]*len(x))for b in a][:-1]+[0]*(n-len(x)));"*(n-1));return[*map(sum,zip(*l))] 

#Python 3, 201 184 bytes

def f(n):x,z,m=[1],[0],n-1;l=[z*m+x+z*m];exec("x=[*map(sum,zip(z+x,x+z))];l.append(z*(n-len(x))+[b for a in zip(x,z*len(x))for b in a][:-1]+z*(n-len(x)));"*m);return[*map(sum,zip(*l))] 

#Python 3, 201 bytes

def f(n):x,l=[1],[[0]*(n-1)+[1]+[0]*(n-1)];exec("x=[*map(sum,zip([0]+x,x+[0]))];l.append([0]*(n-len(x))+[b for a in zip(x,[0]*len(x))for b in a][:-1]+[0]*(n-len(x)));"*(n-1));return[*map(sum,zip(*l))] 

#Python 3, 201 bytes

def f(n):x,l=[1],[[0]*(n-1)+[1]+[0]*(n-1)];exec("x=[*map(sum,zip([0]+x,x+[0]))];l.append([0]*(n-len(x))+[b for a in zip(x,[0]*len(x))for b in a][:-1]+[0]*(n-len(x)));"*(n-1));return[*map(sum,zip(*l))]