A004785 5!(2n-6)!/n!(n-1)! is an integer.

3, 5, 6, 101, 211, 461, 552, 562, 852, 947, 990, 1223, 1432, 1451, 1458, 1506, 1600, 1626, 1892, 2015, 2069, 2147, 2185, 2333, 2480, 2481, 2666, 2994, 3011, 3017, 3356, 3418, 3433, 3442, 3478, 3479, 3485, 3521, 3554, 3566, 3571, 3620, 3628