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%I #46 Nov 26 2015 00:42:58
%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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