A010058 1 if n is a Catalan number else 0.

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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(A000108(n)) = 1, a(A092459(n)) = 0. - Reinhard Zumkeller, Mar 29 2011

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Index entries for characteristic functions

Crossrefs

Cf. A000108, A092459.

Programs

Maple

V:= Array(0..1000):
for n from 1 do
c:= binomial(2*n,n)/(n+1);
  if c > 1000 then break fi;
V[c]:= 1;
od:
convert(V,list); # Robert Israel, Oct 13 2015

Mathematica

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

Formula

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