GCD of the numbers binomial(5*prime(n), 5*k) for k = 1..prime(n)-1.
252, 3003, 2530, 162316, 1749, 196664, 173553, 27683, 2599, 45298, 51491, 408517, 4141, 68927581, 10951, 40172198, 17287, 1860622, 3703559, 25063, 2761517, 2038753, 83, 39427, 257147, 12751553, 105884, 107, 11569953676, 17876939, 5360123519, 85543, 93571
1
It is not clear what the formula is for the highest points in this graph.
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) Table[GCD @@ Table[Binomial[5*n, 5*k], {k, n - 1}], {n, Prime[Range[100]]}]
nonn
T. D. Noe, Oct 27 2015