A028576 a(n) = (1/(4*n)) * Sum_{d|n} mu(n/d) * binomial(2*d, d)^2.

1, 4, 33, 304, 3175, 35556, 420665, 5176000, 65664000, 853367900, 11309870605, 152342891952, 2080240006923, 28738242567524, 401024083514775, 5645275548076800, 80084088088568947, 1143862232096407392, 16437995698573558421, 237520818846111947600, 3449065945198414208745

Offset

1,2

Comments

Conjecture: a(n) is divisible by n and 3*a(n) by n^2. - F. Chapoton, Feb 25 2026

Links

Michel Marcus, Table of n, a(n) for n = 1..800

Mathematica

A028576[n_] := DivisorSum[n, MoebiusMu[n/#]*Binomial[2*#, #]^2 &]/(4*n);
Array[A028576, 25] (* Paolo Xausa, Mar 02 2026 *)

Prog

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(2*d, d)^2)/(4*n) \\ Michel Marcus, Jun 15 2013

Crossrefs

Sequence in context: A123780 A054371 A372897 * A093185 A198006 A339654

Adjacent sequences: A028573 A028574 A028575 * A028577 A028578 A028579

Keyword

nonn

Author

Lionel Levine (levine(AT)ultranet.com)

Status

approved