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%I #6 May 22 2018 11:28:48
%S 1,3,40,1260,72072,6511680,852508800,152512113600,35730097603200,
%T 10613749905158400,3897631650008678400,1733625189541076832000,
%U 918381625086037787136000,571320549624154764994560000
%N Product of next n numbers divided by n.
%e a(4) = (7*8*9*10)/4.
%t f[n_] := Module[{start = Plus @@ Range[n - 1] + 1, end}, end = start + n - 1; (Times @@ Range[start, end])/n]; Table[f[i], {i, 15}]
%t With[{nn=15},Times@@#/Length[#]&/@TakeList[Range[(nn(nn+1))/2], Range[ nn]]] (* Requires Mathematica version 11 or later *) (* _Harvey P. Dale_, May 22 2018 *)
%K nonn
%O 1,2
%A _Amarnath Murthy_, May 13 2004
%E More terms from _Harvey P. Dale_, May 23 2004