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

%I #7 Apr 01 2021 12:17:18

%S 0,2,11,50,214,892,3667,14954,60674,245348,989790,3986292,16034316,

%T 64434424,258740611,1038384154,4165322506,16702230484,66952213546,

%U 268313786524,1075045360756,4306563947464,17249126430766,69078840030340,276613030309204,1107532553770472,4434066076454492

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

%C Since Catalan(n) enumerates so many different things, natural upper bounds like this and A006516 are candidates for counting objects not having some property.

%o (Python)

%o from sympy import catalan

%o def A342906(n): return 2**(2*n-2)-catalan(n) # _Chai Wah Wu_, Apr 01 2021

%Y Cf. A000108, A006516.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Mar 31 2021