A065738 Largest square <= binomial(2n,n).

1, 1, 4, 16, 64, 225, 900, 3364, 12769, 48400, 184041, 703921, 2702736, 10394176, 40106889, 155102116, 601034256, 2333566249, 9075039169, 35345128009, 137845868176, 538256995600, 2104098203601, 8233427666025, 32247599617809, 126410603103009, 495918515715984, 1946939377746496

Offset

0,3

Links

Harry J. Smith, Table of n, a(n) for n = 0..200

Formula

a(n) = A048760(A000984(n)).

a(n) = A192655(n)^2. - Amiram Eldar, Oct 01 2025

Mathematica

a[n_] := Floor[Sqrt[Binomial[2*n, n]]]^2; Array[a, 30, 0] (* Amiram Eldar, Oct 01 2025 *)

Prog

(PARI) a(n) = { sqrtint(binomial(2*n, n))^2 } \\ Harry J. Smith, Oct 29 2009

Crossrefs

Cf. A000984, A048760, A065730-A065741, A192655.

Sequence in context: A189154 A189336 A262334 * A248089 A248088 A294037

Adjacent sequences: A065735 A065736 A065737 * A065739 A065740 A065741

Keyword

easy,nonn

Author

Labos Elemer, Nov 15 2001

Extensions

Terms corrected and extended by Harry J. Smith, Oct 29 2009

a(0) prepended by Amiram Eldar, Oct 01 2025

Status

approved