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

1,1

Links

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A000040, A018252, A203415, A203417.

Sequence in context: A081721 A013009 A301920 * A002218 A107871 A111270

Adjacent sequences: A203413 A203414 A203415 * A203417 A203418 A203419

Keyword

nonn

Author

Clark Kimberling, Jan 01 2012

Status

approved