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a(n) = 2*(n-1)*Catalan(n).
2

%I #17 Nov 10 2024 14:45:31

%S 0,4,20,84,336,1320,5148,20020,77792,302328,1175720,4576264,17829600,

%T 69535440,271455660,1060730100,4148633280,16239715800,63621474840,

%U 249436575960,978650680800,3842267672880,15094623000600,59335590776904,233373427269696

%N a(n) = 2*(n-1)*Catalan(n).

%H Vincenzo Librandi, <a href="/A246574/b246574.txt">Table of n, a(n) for n = 1..1000</a>

%H Igor Pak, <a href="http://arxiv.org/abs/1408.5711">History of Catalan numbers</a>, arXiv:1408.5711 [math.HO], 2014. See Section 5, A_n.

%t Table[2 (CatalanNumber[n] (n - 1)), {n, 1, 30}] (* _Vincenzo Librandi_, Aug 31 2014 *)

%o (Magma) [2*(n-1)*Catalan(n): n in [1..30]]; // _Vincenzo Librandi_, Aug 31 2014

%Y Cf. A000108, A024483.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Aug 30 2014