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a(n) = floor(C(n/2)*C(n/2+1)), where C = Catalan numbers (A000108).
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%I #28 Apr 26 2018 08:41:48

%S 1,1,2,4,10,25,70,199,588,1784,5544,17569,56628,185202,613470,2054998,

%T 6952660,23732911,81662152,283026021,987369656,3465222945,12228193432,

%U 43369190282,154532114800,552998717472,1986841476000,7164993393905,25928281261800,94132464529902

%N a(n) = floor(C(n/2)*C(n/2+1)), where C = Catalan numbers (A000108).

%e k a(k) is prime

%e 2 2

%e 7 199

%e 11 17569

%e 17 23732911

%e 81 102313363987695596246576033222404783284068513

%e 619 200823128294216578246...307006792344011246479 (366 digits)

%t Table[Floor[CatalanNumber[n/2] CatalanNumber[n/2 + 1]], {n, 0, 35}]

%Y Cf. A000108, A005568 (bisection, even part), A005817.

%K nonn

%O 0,3

%A _Vincenzo Librandi_, Apr 11 2018