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Oct 19, 2018 at 11:43 comment added Christian Gaetz Your sequence appears in OEIS. The generating function looks similar to the one for Catalan numbers, and according to one of the comments it is a "Catalan transform" of the Fibonacci numbers.
Oct 19, 2018 at 8:06 comment added Jianrong Li thank you very much. Are there some generalized Catalan number of type B such that the seqnece of the numbers is $3,9,29,97,333$ for $n=2,3,4,5,6$? It seems that the two generalization you gave do not give this sequence.
Oct 19, 2018 at 8:03 vote accept Jianrong Li
Apr 26, 2017 at 20:34 history edited Christian Gaetz CC BY-SA 3.0
Added a reference
Apr 26, 2017 at 17:31 history answered Christian Gaetz CC BY-SA 3.0