The product of the composite numbers in the first prime gap having 2*n - 1 numbers.
1, 4, 720, 11793600, 60072730099200, 26584832627940787200, 26836382332895254479360000, 1063186156509747740870400000, 9304819656528376743991389905860426337114959872000, 21886922063220799218562795688752620430540800000
0
We set the zeroth term to 1 because there are no numbers between 2 and 3.
T. D. Noe, Plot of 70 terms
T. D. Noe, Table of 70 terms
(Mma) nn = 19; t = Table[0, {nn}]; p = 3; found = 0; While[found < nn, nextP = NextPrime[p]; diff = (nextP - p)/2; If[diff <= nn && t[[diff]] == 0, t[[diff]] = Times @@ Range[p+1, nextP-1]; found++]; p = nextP]; t = Join[{1}, t]
Cf. A000230.
nonn
T. D. Noe, May 04 2015