A010058 - OEIS

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

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OFFSET

0,1

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

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

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 *)

CROSSREFS

Cf. A000108, A092459.

Sequence in context: A023959 A341334 A076182 * A140591 A189476 A288752

Adjacent sequences: A010055 A010056 A010057 * A010059 A010060 A010061

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved