Given the sequence $$a_k=\frac{(2k)!}{4^k(k!)^2(2k+1)}(0.5)^{2k+1},$$ I should find a recurrence relation for it. I came up with $a_0 = 0.5$ and $$a_{k+1}=\frac{(2k+1)^2}{8(k+1)(2k+3)}a_k.$$ is there an optimized version of this recurrence relation?
2026-03-30 02:03:37.1774836217
Optimizing a recurrence relation for a sequence
36 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in SEQUENCES-AND-SERIES
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