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A simple hypergeometric function fails.

There is a nice method to compute the Narayana polynomials. With Maple we can write

P := n -> simplify(hypergeom([-n,-n+1], [2], 1/x));
seq(expand(x^k*P(k)), k=0..5);

and get the answer

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.

Trying the same with Sage

P = lambda n: simplify(hypergeometric([-n,-n+1],[2], 1/x))
[expand(x^k*P(k)) for k in (0..5)]

gives the answer

[1, x, ..., x^n*hypergeometric((-n, -n-1),(2),1/x)]

This is really disappointing. Is there a workaround?

A simple hypergeometric function fails.

There is a nice method to compute the Narayana polynomials. With Maple we can write

P := n -> simplify(hypergeom([-n,-n+1], [2], 1/x));
seq(expand(x^k*P(k)), k=0..5);

and get the answer

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.

Trying the same with Sage

P = lambda n: simplify(hypergeometric([-n,-n+1],[2], 1/x))
[expand(x^k*P(k)) for k in (0..5)]

gives the answer

[1, x, ..., x^n*hypergeometric((-n, -n-1),(2),1/x)]

This is really disappointing. Is there a workaround?