A203315 - OEIS

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A203315

Vandermonde determinant of the first n odd primes.

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

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OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A203316, A203317, A000040.

Sequence in context: A132569 A165644 A338005 * A158506 A167435 A270124

Adjacent sequences: A203312 A203313 A203314 * A203316 A203317 A203318

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 01 2012

STATUS

approved