A028576 - OEIS

%I #22 Mar 02 2026 18:22:38

%S 1,4,33,304,3175,35556,420665,5176000,65664000,853367900,11309870605,

%T 152342891952,2080240006923,28738242567524,401024083514775,

%U 5645275548076800,80084088088568947,1143862232096407392,16437995698573558421,237520818846111947600,3449065945198414208745

%N a(n) = (1/(4*n)) * Sum_{d|n} mu(n/d) * binomial(2*d, d)^2.

%C Conjecture: a(n) is divisible by n and 3*a(n) by n^2. - _F. Chapoton_, Feb 25 2026

%H Michel Marcus, <a href="/A028576/b028576.txt">Table of n, a(n) for n = 1..800</a>

%t A028576[n_] := DivisorSum[n, MoebiusMu[n/#]*Binomial[2*#, #]^2 &]/(4*n);

%t Array[A028576, 25] (* _Paolo Xausa_, Mar 02 2026 *)

%o (PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(2*d, d)^2)/(4*n) \\ _Michel Marcus_, Jun 15 2013

%K nonn

%O 1,2

%A Lionel Levine (levine(AT)ultranet.com)