Please consider
def H(n,k): return hypergeometric([-k, -n + k], [-k], -1)
def T(n,k): return int(H(n,k).n())
def S(n,k): return H(n,k).simplify_hypergeometric()
for n in range(8):
print([T(n, k) for k in range(n+1)])
print([S(n, k) for k in range(n+1)])
The result:
[1] [1] [1, 1] [2, 1] [1, 2, 1] [4, 2, 1] [1, 3, 2, 1] [8, 4, 2, 1]
I expected the same result in both cases. Note that both Maple and
Mathematika return the first variant, T(n, k), probably indicating a
problem in simplify_hypergeometric()? [Windows 64, Sage 9.3]
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