A302093 a(n) = floor(C(n/2)*C(n/2+1)), where C = Catalan numbers (A000108).

1, 1, 2, 4, 10, 25, 70, 199, 588, 1784, 5544, 17569, 56628, 185202, 613470, 2054998, 6952660, 23732911, 81662152, 283026021, 987369656, 3465222945, 12228193432, 43369190282, 154532114800, 552998717472, 1986841476000, 7164993393905, 25928281261800, 94132464529902

Offset: 0

Author

Vincenzo Librandi, Apr 11 2018

Keywords

• nonn

Examples

			k         a(k) is prime
2          2
7          199
11         17569
17         23732911
81         102313363987695596246576033222404783284068513
619        200823128294216578246...307006792344011246479 (366 digits)
		

Links

• Robert Israel, Table of n, a(n) for n = 0..1667

Crossrefs

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

Programs

Maple

a108:= n -> binomial(2*n,n)/(n+1):
seq(floor(a108(n/2)*a108(n/2+1)),n=0..40); # Robert Israel, May 12 2025

Mathematica

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