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Aug 27, 2021 at 23:07 history edited Pietro Majer CC BY-SA 4.0
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Aug 27, 2021 at 22:45 comment added Pietro Majer So the above identity can be written as $$P_n = 4^{-n}\sum_{k=0}^n{2k \choose k}{2n-2k\choose n-k}T_{2n-k} $$ which has to be for sure well-known, although I do not find it around right now
Aug 27, 2021 at 22:37 history answered Pietro Majer CC BY-SA 4.0