A203418 Vandermonde determinant of the first n composite numbers (A002808).

1, 2, 16, 240, 11520, 13271040, 254803968000, 15892123484160000, 5126163351050649600000, 89288743527804466888704000000, 50689719717698351557731837542400000000, 125765178831579421305165126665125232640000000000

Offset

1,2

Comments

Each term divides its successor, as in A203419, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203420.

Links

G. C. Greubel, Table of n, a(n) for n = 1..42

Mathematica

composite = Select[Range[100], CompositeQ]; (* A002808 *)
z = 20;
f[j_]:= composite[[j]];
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, z}]             (* this sequence *)
Table[v[n+1]/v[n], {n, z}]      (* A203419 *)
Table[v[n]/d[n], {n, z}]        (* A203420 *)

Prog

(Magma)
A002808:=[n: n in [2..250] | not IsPrime(n)];
a:= func< n | n eq 0 select 1 else (&*[(&*[A002808[k+2] - A002808[j+1]: j in [0..k]]): k in [0..n-1]]) >;
[a(n): n in [0..20]]; // G. C. Greubel, Feb 24 2024
(SageMath)
A002808=[n for n in (2..250) if not is_prime(n)]
def a(n): return product(product( A002808[k+1] - A002808[j] for j in range(k+1)) for k in range(n))
[a(n) for n in range(15)] # G. C. Greubel, Feb 24 2024

Crossrefs

Cf. A000040, A000178, A002808, A203419, A203420.

Sequence in context: A206884 A188756 A156495 * A207082 A207176 A217812

Adjacent sequences: A203415 A203416 A203417 * A203419 A203420 A203421

Keyword

nonn

Author

Clark Kimberling, Jan 02 2012

Status

approved