GCD of the numbers binomial(2*n, 2*k) for k = 1..n-1.
1, 6, 15, 14, 15, 33, 91, 2, 51, 19, 11, 23, 65, 3, 435, 62, 17, 3, 703, 1, 41, 43, 23, 47, 35, 1, 159, 7, 29, 59, 1891, 2, 1, 67, 1, 71, 2701, 1, 1, 79, 123, 249, 43, 1, 267, 1, 47, 1, 679, 1, 101, 103, 53, 321, 109, 1, 113, 1, 59, 1, 671, 1, 5, 254, 5, 1441, 67
1
See S000731 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[2*n, 2*k], {k, n - 1}], {n, 2, 100}]]
nonn
T. D. Noe, Oct 27 2015