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a(n) = mu(n) * Catalan(n).
1

%I #17 Jan 30 2022 14:08:39

%S 1,1,-2,-5,0,-42,132,-429,0,0,16796,-58786,0,-742900,2674440,9694845,

%T 0,-129644790,0,-1767263190,0,24466267020,91482563640,-343059613650,0,

%U 0,18367353072152,0,0,-1002242216651368,-3814986502092304,-14544636039226909,0,212336130412243110

%N a(n) = mu(n) * Catalan(n).

%H Harry J. Smith, <a href="/A062627/b062627.txt">Table of n, a(n) for n = 0..200</a>

%F mu(n)* binomial(2*n, n)/(n+1); or mu(n) * A000108(n).

%t Join[{1},Table[MoebiusMu[n]CatalanNumber[n],{n,40}]] (* _Harvey P. Dale_, Jan 30 2022 *)

%o (PARI) a(n)={if(n==0, 1, moebius(n)*binomial(2*n, n)/(n + 1))}

%Y Cf. A000108.

%K easy,sign

%O 0,3

%A _Jason Earls_, Jul 04 2001