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
Offset: 1
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PARI
a(n) = sumdiv(n, d, moebius(n/d)*binomial(2*d, d)^2)/(4*n) \\ Michel Marcus, Jun 15 2013