A203419 a(n) = A203418(n+1)/A203418(n).

2, 8, 15, 48, 1152, 19200, 62370, 322560, 17418240, 567705600, 2481078600, 16907304960, 1504935936000, 8799558768000, 76435881984000, 819678899239200, 10176845001523200, 2169274855587840000, 215013524533936128000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..350

Crossrefs

Cf. A000040, A002808, A003418, A203418, A203420.

Programs

Magma

A002808:=[n: n in [2..250] | not IsPrime(n)];
a:= func< n | (&*[A002808[n+1] - A002808[j+1]: j in [0..n-1]]) >;
[a(n): n in [1..40]]; // G. C. Greubel, Feb 24 2024

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}]           (* A203418 *)
Table[v[n+1]/v[n], {n,z}]    (* this sequence *)
Table[v[n]/d[n], {n,z}]      (* A203420 *)

SageMath

A002808=[n for n in (2..250) if not is_prime(n)]
def a(n): return product(A002808[n] - A002808[j] for j in range(n))
[a(n) for n in range(1,41)] # G. C. Greubel, Feb 24 2024