A203315 Vandermonde determinant of the first n odd primes.

1, 2, 16, 3072, 2949120, 118908518400, 30684105356083200, 509012486930992988160000, 1448974328493266972309245132800000, 24498250851046882007528282887645298688000000, 120709538882209643641596013856771385957962848665600000000

Offset: 1

Author

Clark Kimberling, Jan 01 2012

Keywords

• nonn

Comments

Each term divides its successor, as in A203316, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203317.

Examples

			v(3)=(5-3)(7-3)(7-5)=16.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..35

Crossrefs

Cf. A203316, A203317, A000040.

Programs

Maple

Primes:=3:
A[1]:= 1:
for n from 2 to 20 do
  Primes:=  Primes, ithprime(n+1);
  A[n]:= A[n-1] * mul(Primes[n]-Primes[i],i=1..n-1);
od:
seq(A[i],i=1..20);# Robert Israel, Apr 08 2019

Mathematica

f[j_] := Prime[j + 1]; z = 17;
v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}]
Table[v[n], {n, 1, z}]                  (* A203315 *)
Table[v[n + 1]/(2 v[n]), {n, 1, z - 1}] (* A203316 *)
Table[v[n]/d[n], {n, 1, 20}]            (* A203317 *)