GCD of the numbers binomial(5*n, 5*k) for k = 1..n-1.
1, 252, 3003, 1292, 2530, 261, 162316, 1924, 58179, 658, 1749, 59, 196664, 21574, 191771, 316, 173553, 801, 27683, 194, 72821, 34989, 2599, 1, 4264205, 21844, 289641, 38086, 45298, 149, 51491, 33284, 220539, 2171, 173, 179, 408517, 3, 46484243, 78406
1
See S000737 for the sequence obtained when n is restricted to prime numbers.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Carl McTague, On the greatest common divisor of binomial(qn,q), binomial(qn,2q),..., binomial(qn,qn-q), arXix 1510.06696 (Oct 22 2015).
(Mma) Join[{1}, Table[GCD @@ Table[Binomial[5*n, 5*k], {k, n - 1}], {n, 2, 100}]]
nonn
T. D. Noe, Oct 27 2015