A203315
Vandermonde determinant of the first n odd primes.
Original entry on oeis.org
1, 2, 16, 3072, 2949120, 118908518400, 30684105356083200, 509012486930992988160000, 1448974328493266972309245132800000, 24498250851046882007528282887645298688000000, 120709538882209643641596013856771385957962848665600000000
Offset: 1
-
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
-
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 *)
A203316
a(n) = v(n+1)/(2*v(n)), where v=A203315.
Original entry on oeis.org
1, 4, 96, 480, 20160, 129024, 8294400, 1423319040, 8453652480, 2463635865600, 89117289676800, 660834091008000, 63038756487168000, 20712734274355200000, 4023397460155878604800, 27460572284725493760000
Offset: 1
-
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 *)
Original entry on oeis.org
1, 8, 480, 322560, 1857945600, 137339338752000, 90498933234597888000, 806410654352196092559360000, 151104996166246050391298219704320000, 278316545034703677313682486677538340864000000
Offset: 1
-
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}] (* A000178 *)
Table[v[n], {n, 1, z}] (* A203524 *)
Table[v[n + 1]/(8 v[n]), {n, 1, z - 1}] (* A203525 *)
Table[v[n]/d[n], {n, 1, 20}] (* A203526 *)
Showing 1-3 of 3 results.
Comments