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

%I A120624 #16 Aug 30 2016 16:41:12
%S A120624 6,28,42,45,66,77,91,110,126,140,153,156,170,187,190,204,209,210,220,
%T A120624 228,231,238,266,276,299,308,312,315,322,325,330,345,378,414,420,429,
%U A120624 435,440,442,450,459,460,468,476,483,493,496,510,527,551,558,561,570
%N A120624 Numbers n such that the n-th Catalan number C(2n,n)/(n+1) is divisible by 2n.
%C A120624 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
%H A120624 Chai Wah Wu, <a href="/A120624/b120624.txt">Table of n, a(n) for n = 1..10000</a>
%t A120624 fQ[n_] := fQ[n_] := IntegerQ[ Binomial[2n, n]/(2n(n + 1))]; Select[ Range@8719, fQ@# &]
%t A120624 Select[Range[600],Divisible[CatalanNumber[#],2#]&] (* _Harvey P. Dale_, Aug 30 2016 *)
%o A120624 (Python)
%o A120624 from __future__ import division
%o A120624 A120624_list, b = [], 1
%o A120624 for n in range(1,10**5):
%o A120624     if not b % (2*n):
%o A120624         A120624_list.append(n)
%o A120624     b = b*(4*n+2)//(n+2) # _Chai Wah Wu_, Mar 25 2016
%Y A120624 Subset of A014847.
%Y A120624 Cf. A120622.
%K A120624 nonn
%O A120624 1,1
%A A120624 _Robert G. Wilson v_, Jun 19 2006
%E A120624 Definition corrected by _Joel B. Lewis_, Apr 30 2009