A203522 a(n) = v(n+1)/v(n), where v = A203521.

1, 5, 56, 1080, 52416, 2073600, 168537600, 9963233280, 1122750720000, 234209649623040, 22056529195008000, 5634088861040640000, 1027073825689514803200, 132063784535221862400000, 27917533370401003929600000

Offset: 0

Author

Clark Kimberling, Jan 03 2012

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..290
• Robert Israel, Table of n, a(n) for n = 1..290

Crossrefs

Cf. A203522, A203523, A000040, A093883.

Programs

Maple

f:= proc(n) local i; mul(ithprime(i)+ithprime(n+1),i=1..n) end proc:
map(f, [$1..30]); # Robert Israel, Jan 28 2025

Mathematica

f[j_] := Prime[j]; z = 15;
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}]                (* A203521 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]   (* A203522 *)
Table[v[n]/d[n], {n, 1, 20}]          (* A203523 *)

Formula

a(n) = Product_{i=1..n} (prime(i)+prime(n+1)). - Robert Israel, Jan 28 2025

Extensions

a(0) = 1 inserted by Robert Israel, Jan 29 2025