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A120624
Numbers n such that the n-th Catalan number C(2n,n)/(n+1) is divisible by 2n.
3
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
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
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jun 19 2006
EXTENSIONS
Definition corrected by Joel B. Lewis, Apr 30 2009
STATUS
approved