##Python 2, 55 bytes
def f(x,n):l=[1]*n;exec"print l[0];l=l[1:]+[sum(l)];"*x
Tracks a length-n window of the sequence in the list l, updated by appending the sum and removing the first element. Prints the first element each iteration for x iterations.
A different approach of storing all the elements and summing the last n values gave the same length (55).
def f(x,n):l=[1]*n;exec"l+=sum(l[-n:]),;"*x;print l[:x]