This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A262204 #25 Sep 08 2022 08:46:14 %S A262204 12,120,30240,17297280,28158588057600,64764752532480000, %T A262204 830034394580628357120000,4299578163927654889881600000, %U A262204 212850788988365112429784203264000000,265847614191284935213187014536606662000640000000 %N A262204 a(n) = (2*prime(n))! / prime(n)!. %C A262204 Inspired by simplicity of sequence formula that is (p + p)!/p! where p is n-th prime number. %F A262204 a(n) = 2 * A075069(n). %F A262204 a(n) = A001813(prime(n)). - _Michel Marcus_, Sep 20 2015 %F A262204 a(n) mod A039716(n) = 0. %e A262204 For n=1, a(n) = (2*prime(n))! / prime(n)! = 4!/2! = 3*4 = 12. %e A262204 For n=2, a(n) = (2*prime(n))! / prime(n)! = 6!/3! = 4*5*6 = 120. %e A262204 For n=3, a(n) = (2*prime(n))! / prime(n)! = 10!/5! = 6*7*8*9*10 = 30240. %o A262204 (PARI) a(n) = (2*prime(n))!/prime(n)!; %o A262204 vector(10, n, a(n)) %o A262204 (Magma) [Factorial(NthPrime(n)+NthPrime(n)) / Factorial(NthPrime(n)): n in [1..10]]; // _Vincenzo Librandi_, Sep 16 2015 %Y A262204 Cf. A001813, A039716, A100484, A075069, A262206. %K A262204 nonn,easy %O A262204 1,1 %A A262204 _Altug Alkan_, Sep 15 2015