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

0,3

Links

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

Formula

a(n) ~ 2^(2*n+5) / (n^3 * Pi). - Amiram Eldar, Oct 01 2025

Example

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

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}]

Crossrefs

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

Sequence in context: A339295 A001998 A005817 * A292617 A148093 A206289

Adjacent sequences: A302090 A302091 A302092 * A302094 A302095 A302096

Keyword

nonn

Author

Vincenzo Librandi, Apr 11 2018

Status

approved