A203416 a(n) = A203415(n+1)/A203415(n).

3, 10, 56, 120, 432, 12672, 249600, 873180, 4838400, 296110080, 10786406400, 49621572000, 355053404160, 34613526528000, 211189410432000, 1910897049600000, 21311651380219200, 274774815041126400, 62908970812047360000

Offset: 1

Author

Clark Kimberling, Jan 01 2012

Keywords

• nonn

Links

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

Crossrefs

Cf. A000040, A018252, A203415, A203417.

Programs

Magma

A018252:=[n : n in [1..250] | not IsPrime(n) ];
A203416:= func< n | n eq 1 select 3 else (&*[A018252[n+1] - A018252[j+1]: j in [0..n-1]]) >;
[A203416(n): n in [1..30]]; // G. C. Greubel, Feb 29 2024

Mathematica

z=20;
nonprime = Join[{1}, Select[Range[250], CompositeQ]]; (* A018252 *)
f[j_]:= nonprime[[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,1,z}]             (* A203415 *)
Table[v[n+1]/v[n], {n,1,z}]      (* this sequence *)
Table[v[n]/d[n], {n,1,z}]        (* A203417 *)

SageMath

A018252=[n for n in (1..250) if not is_prime(n)]
def A203416(n): return product(A018252[n]-A018252[j] for j in range(n))
[A203416(n) for n in range(1,31)] # G. C. Greubel, Feb 29 2024