cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A010058 1 if n is a Catalan number else 0.

This page as a plain text file.
%I A010058 #46 Nov 26 2015 00:42:58
%S A010058 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 A010058 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 A010058 0,0,0,0,0,0,0,0,0,0,0,0,0
%N A010058 1 if n is a Catalan number else 0.
%C A010058 a(A000108(n)) = 1, a(A092459(n)) = 0. - _Reinhard Zumkeller_, Mar 29 2011
%H A010058 Robert Israel, <a href="/A010058/b010058.txt">Table of n, a(n) for n = 0..10000</a>
%H A010058 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F A010058 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 A010058 V:= Array(0..1000):
%p A010058 for n from 1 do
%p A010058 c:= binomial(2*n,n)/(n+1);
%p A010058   if c > 1000 then break fi;
%p A010058 V[c]:= 1;
%p A010058 od:
%p A010058 convert(V,list); # _Robert Israel_, Oct 13 2015
%t A010058 t = CatalanNumber@ Range@ 12; Table[Boole@ MemberQ[t, n], {n, 0, 96}] (* _Michael De Vlieger_, Sep 29 2015 *)
%Y A010058 Cf. A000108, A092459.
%K A010058 nonn
%O A010058 0,1
%A A010058 _N. J. A. Sloane_