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Central numbers in a Moebius-binomial triangle.
3

%I #11 Jan 24 2024 01:21:12

%S 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,

%T 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,

%U 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

%N Central numbers in a Moebius-binomial triangle.

%C Central numbers in A105595.

%C There seems to be a typo in above comment, maybe A105594 was intended? - _Antti Karttunen_, Aug 27 2017

%C Partial sums are A105598.

%H Antti Karttunen, <a href="/A105597/b105597.txt">Table of n, a(n) for n = 0..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

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

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

%o (PARI) A105597(n) = if(n<2,1,binomial(abs(moebius(n)), abs(moebius(n\2)))); \\ _Antti Karttunen_, Aug 27 2017

%K easy,nonn

%O 0,1

%A _Paul Barry_, Apr 14 2005