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 A010058 1 if n is a Catalan number else 0. 3

%I

%S 0,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0

%N 1 if n is a Catalan number else 0.

%C a(A000108(n)) = 1, a(A092459(n)) = 0. - _Reinhard Zumkeller_, Mar 29 2011

%H Robert Israel, <a href="/A010058/b010058.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = abs(sgn(n - sup((2*k)!/(k!*(k + 1)!))) - 1), for n - (2*k)!/(k!*(k + 1)!) >= 0. - _Ilya Gutkovskiy_, Sep 27 2015

%p V:= Array(0..1000):

%p for n from 1 do

%p c:= binomial(2*n,n)/(n+1);

%p if c > 1000 then break fi;

%p V[c]:= 1;

%p od:

%p convert(V,list); # _Robert Israel_, Oct 13 2015

%t t = CatalanNumber@ Range@ 12; Table[Boole@ MemberQ[t, n], {n, 0, 96}] (* _Michael De Vlieger_, Sep 29 2015 *)

%Y Cf. A000108, A092459.

%K nonn

%O 0,1

%A _N. J. A. Sloane_

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Last modified October 23 05:49 EDT 2018. Contains 316519 sequences. (Running on oeis4.)