a := n -> hypergeom([-n, -n, n + 1, n + 1], [1/2, 1, 1], 1/4);
seq(simplify(a(n)), n=0..5);
seq(simplify((-1)^n*a(n)), n=0..5);
1, 3, 25, 243, 2601, 29403
1, -2, 25, -242, 2601, -29402
I see the following, in each release from Maple 17.00 (Feb 2013) to Maple 2017.3 (Sep 2017).
a := n -> hypergeom([-n, -n, n + 1, n + 1], [1/2, 1, 1], 1/4): seq(simplify(a(n)), n=0..5);
1, 3, 25, 243, 2601, 29403
seq(simplify((-1)^n*a(n)), n=0..5);
1, -3, 25, -243, 2601, -29403
I see the following, in each release from Maple 17.00 (Feb 2013) to Maple 2017.3 (Sep 2017).
a := n -> hypergeom([-n, -n, n + 1, n + 1], [1/2, 1, 1], 1/4): seq(simplify(a(n)), n=0..5);
1, 3, 25, 243, 2601, 29403
seq(simplify((-1)^n*a(n)), n=0..5);
1, -3, 25, -243, 2601, -29403
Good to hear. And what do earlier releases show?
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