A262204 - OEIS

%I #25 Sep 08 2022 08:46:14

%S 12,120,30240,17297280,28158588057600,64764752532480000,

%T 830034394580628357120000,4299578163927654889881600000,

%U 212850788988365112429784203264000000,265847614191284935213187014536606662000640000000

%N a(n) = (2*prime(n))! / prime(n)!.

%C Inspired by simplicity of sequence formula that is (p + p)!/p! where p is n-th prime number.

%F a(n) = 2 * A075069(n).

%F a(n) = A001813(prime(n)). - _Michel Marcus_, Sep 20 2015

%F a(n) mod A039716(n) = 0.

%e For n=1, a(n) = (2*prime(n))! / prime(n)! = 4!/2! = 3*4 = 12.

%e For n=2, a(n) = (2*prime(n))! / prime(n)! = 6!/3! = 4*5*6 = 120.

%e For n=3, a(n) = (2*prime(n))! / prime(n)! = 10!/5! = 6*7*8*9*10 = 30240.

%o (PARI) a(n) = (2*prime(n))!/prime(n)!;

%o vector(10, n, a(n))

%o (Magma) [Factorial(NthPrime(n)+NthPrime(n)) / Factorial(NthPrime(n)): n in [1..10]]; // _Vincenzo Librandi_, Sep 16 2015

%Y Cf. A001813, A039716, A100484, A075069, A262206.

%K nonn,easy

%O 1,1

%A _Altug Alkan_, Sep 15 2015