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%I #45 Sep 08 2022 08:46:14
%S 2,24,2520,604800,54486432000,53353114214400,35905578804006912000,
%T 80018147048929689600000,203939450748460387344384000000,
%U 1441310123089178548721360295690240000000,9218619547278385997621820451234775040000000
%N Product of prime(n) consecutive numbers starting from n.
%C a(n) is always divisible by A039716(n).
%F a(n) = (prime(n) + n - 1)! / (n-1)!.
%e For n=1, a(1) = 1*2 = 2.
%e For n=2, a(2) = 2*3*4 = 24.
%e For n=3, a(3) = 3*4*5*6*7 = 2520.
%e For n=4, a(4) = 4*5*6*7*8*9*10 = 604800.
%p A262206:=n->(ithprime(n)+n-1)! / (n-1)!: seq(A262206(n), n=1..15); # _Wesley Ivan Hurt_, Sep 15 2015
%t Table[(Prime[n] + n - 1)!/(n - 1)!, {n, 15}] (* _Michael De Vlieger_, Sep 15 2015 *)
%o (PARI) a(n) = (prime(n)+n-1)! / (n-1)!;
%o vector(15,n,a(n))
%o (PARI) a(n)=factorback([n..n+prime(n)-1]) \\ _Charles R Greathouse IV_, Sep 21 2015
%o (Magma) [Factorial(NthPrime(n)+n-1)/Factorial(n-1): n in [1..15]]; // _Vincenzo Librandi_, Sep 16 2015
%Y Cf. A075069: product of prime(n) consecutive numbers starting from prime(n).
%Y Cf. A014688, A039716, A075068, A262204.
%K nonn,easy
%O 1,1
%A _Altug Alkan_, Sep 15 2015
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