A139161 a(n)=(prime(n)!+3)/3.
3, 41, 1681, 13305601, 2075673601, 118562476032001, 40548366802944001, 8617338912961658880001, 2947253997913233984847872000001, 2740946218059307605908520960000001
Offset: 2
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Mathematica
Table[(Prime[n]! + 3)/3, {n, 2, 30}]