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A203315 Vandermonde determinant of the first n odd primes. 6
1, 2, 16, 3072, 2949120, 118908518400, 30684105356083200, 509012486930992988160000, 1448974328493266972309245132800000, 24498250851046882007528282887645298688000000, 120709538882209643641596013856771385957962848665600000000 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A132569 A165644 A338005 * A158506 A167435 A270124
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 01 2012
STATUS
approved

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Last modified July 18 18:59 EDT 2024. Contains 374388 sequences. (Running on oeis4.)