A186546 Floor-Sqrt transform of Catalan numbers (A000108).

1, 1, 1, 2, 3, 6, 11, 20, 37, 69, 129, 242, 456, 861, 1635, 3113, 5946, 11386, 21854, 42038, 81019, 156416, 302460, 585712, 1135739, 2204982, 4285715, 8338678, 16240318, 31658209, 61765576, 120601144, 235656667, 460799447, 901634095, 1765300397, 3458294143, 6778702259

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..89

Formula

a(n) = floor(sqrt(binomial(2*n,n)/(n+1))).

a(n) ~ 2^n / (n^(3/4) * Pi^(1/4)). - Amiram Eldar, Oct 03 2025

Mathematica

Table[Floor[Sqrt[Binomial[2n, n]/(n+1)]], {n, 0, 100}]

Prog

(Maxima) makelist(floor(sqrt(binomial(2*n, n)/(n+1))), n, 0, 24);
(PARI) a(n) = sqrtint(binomial(2*n, n)/(n+1)); \\ Michel Marcus, Oct 03 2025

Crossrefs

Cf. A000108.

Sequence in context: A047081 A115792 A054177 * A318910 A141435 A096080

Adjacent sequences: A186543 A186544 A186545 * A186547 A186548 A186549

Keyword

nonn,easy

Author

Emanuele Munarini, Jul 07 2011

Status

approved