A105597 Central numbers in a Moebius-binomial triangle.

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Paul Barry, Apr 14 2005

Keywords

• easy
• nonn

Comments

Central numbers in A105595.

There seems to be a typo in above comment, maybe A105594 was intended? - Antti Karttunen, Aug 27 2017

Partial sums are A105598.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for characteristic functions

Programs

Mathematica

a[n_]:= Binomial[Abs[MoebiusMu[n]],Abs[MoebiusMu[Floor[n/2]]]];Table[a[n],{n,0,100}] (* James C. McMahon, Jan 23 2024 *)

PARI

A105597(n) = if(n<2,1,binomial(abs(moebius(n)), abs(moebius(n\2)))); \\ Antti Karttunen, Aug 27 2017

Formula

a(n) = binomial(abs(mu(n)), abs(mu(floor(n/2)))).