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a(n) is the value of Vandermonde determinant for lexicographically earliest n-mark Golomb-ruler.
0

%I #7 Apr 04 2015 21:50:42

%S 1,1,6,720,6652800,1693749657600,367216146859161600000,

%T 1888288177044984240734208000000,

%U 4157567140515322460268246337585152000000000

%N a(n) is the value of Vandermonde determinant for lexicographically earliest n-mark Golomb-ruler.

%F a(n)=Product[a(i)-a(j)], j<i<=n; product of C[n, 2] positive differences provided by the n marks of ruler.

%e n=6:the ruler={1,2,5,11,13,18}, the C[6,2]=15 possible differences={17,16,13,7,5,12,11,8,2,10,9,6,4,3,1}; the product = a(6)=1693749657600.

%t t={marks of ruler}; lt=Length[t] b[x_] := Part[t, x] bd[x_] := Reverse[b[x]-Table[b[j], {j, 1, x-1}]] pb[x_] := Apply[Times, bd[x]] Table[{j, bd[j], pb[j]}, {j, 1, lt}]; vm=Table[Apply[Times, Table[pb[u], {u, 1, k}]], {k, 1, lt}]; Part[vm, lt]

%Y Cf. A031869-A031875.

%K nonn

%O 1,3

%A _Labos Elemer_, Feb 24 2003