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A203315 Vandermonde determinant of the first n odd primes.

%I A203315 #8 Apr 08 2019 11:08:34
%S A203315 1,2,16,3072,2949120,118908518400,30684105356083200,
%T A203315 509012486930992988160000,1448974328493266972309245132800000,
%U A203315 24498250851046882007528282887645298688000000,120709538882209643641596013856771385957962848665600000000
%N A203315 Vandermonde determinant of the first n odd primes.
%C A203315 Each term divides its successor, as in A203316, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203317.
%H A203315 Robert Israel, <a href="/A203315/b203315.txt">Table of n, a(n) for n = 1..35</a>
%e A203315 v(3)=(5-3)(7-3)(7-5)=16.
%p A203315 Primes:=3:
%p A203315 A[1]:= 1:
%p A203315 for n from 2 to 20 do
%p A203315   Primes:=  Primes, ithprime(n+1);
%p A203315   A[n]:= A[n-1] * mul(Primes[n]-Primes[i],i=1..n-1);
%p A203315 od:
%p A203315 seq(A[i],i=1..20);# _Robert Israel_, Apr 08 2019
%t A203315 f[j_] := Prime[j + 1]; z = 17;
%t A203315 v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]
%t A203315 d[n_] := Product[(i - 1)!, {i, 1, n}]
%t A203315 Table[v[n], {n, 1, z}]                  (* A203315 *)
%t A203315 Table[v[n + 1]/(2 v[n]), {n, 1, z - 1}] (* A203316 *)
%t A203315 Table[v[n]/d[n], {n, 1, 20}]            (* A203317 *)
%Y A203315 Cf. A203316, A203317, A000040.
%K A203315 nonn
%O A203315 1,2
%A A203315 _Clark Kimberling_, Jan 01 2012