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You can try with sympy :

sage: import sympy
sage: P = lambda n: sympy.hyper([-n,-n+1],[2], 1/x).simplify()
sage: [expand(x^k*P(k)) for k in (0..5)]
[1,
 x,
 x^2 + x,
 x^3 + 3*x^2 + x,
 x^4 + 6*x^3 + 6*x^2 + x,
 x^5 + 10*x^4 + 20*x^3 + 10*x^2 + x]