A120624 Numbers n such that the n-th Catalan number C(2n,n)/(n+1) is divisible by 2n.

6, 28, 42, 45, 66, 77, 91, 110, 126, 140, 153, 156, 170, 187, 190, 204, 209, 210, 220, 228, 231, 238, 266, 276, 299, 308, 312, 315, 322, 325, 330, 345, 378, 414, 420, 429, 435, 440, 442, 450, 459, 460, 468, 476, 483, 493, 496, 510, 527, 551, 558, 561, 570

Offset

1,1

Comments

Equivalently, numbers such that the n-th central binomial coefficient C(2n, n) is divisible by 2n(n + 1). - Joel B. Lewis, Jan 07 2008

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Mathematica

fQ[n_] := fQ[n_] := IntegerQ[ Binomial[2n, n]/(2n(n + 1))]; Select[ Range@8719, fQ@# &]
Select[Range[600], Divisible[CatalanNumber[#], 2#]&] (* Harvey P. Dale, Aug 30 2016 *)

Prog

(Python)
from __future__ import division
A120624_list, b = [], 1
for n in range(1, 10**5):
    if not b % (2*n):
        A120624_list.append(n)
    b = b*(4*n+2)//(n+2) # Chai Wah Wu, Mar 25 2016

Crossrefs

Subset of A014847.

Cf. A120622.

Sequence in context: A295078 A055196 A323752 * A138873 A377095 A091307

Adjacent sequences: A120621 A120622 A120623 * A120625 A120626 A120627

Keyword

nonn

Author

Robert G. Wilson v, Jun 19 2006

Extensions

Definition corrected by Joel B. Lewis, Apr 30 2009

Status

approved