A060381 - OEIS

%I #27 Mar 07 2020 01:39:38

%S 1,2,15,385,17017,1062347,86822723,10131543907,1204461778591,

%T 198229051666003,35224440615606707,6295457783127226289,

%U 1331590860773071702483,310692537866322378582047,78832548083496383033878901,21381953681344611984282084241

%N a(n) = prime(n)*prime(n+1)*...*prime(2*n-1), where prime(i) is the i-th prime.

%C Central terms of triangle A098012. - _Reinhard Zumkeller_, Oct 02 2014

%C For n >= 0, a(n+1) is the n-th power of 15 in the monoid defined by A306697. - _Peter Munn_, Feb 18 2020

%H Reinhard Zumkeller, <a href="/A060381/b060381.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) = A002110(2*n-1)/A002110(n-1). - _Michel Marcus_, Mar 16 2019

%F From _Peter Munn_, Feb 18 2020: (Start)

%F a(n) = A019565(A006516(n)).

%F For n >= 1, a(n) = A098012(n,n), reading A098012 as a square array.

%F For n > 1, a(n) = A306697(a(n-1), 15) = A059896(A003961^2(a(n-1)), A003961(a(n-1))).

%F (End)

%e a(1)=2; a(2) = 3*5 = 15; a(3) = 5*7*11 = 385.

%p seq(mul(ithprime(n+k),k=0..n-1),n=0..15); # _Muniru A Asiru_, Mar 16 2019

%t Table[Times@@Prime[Range[n,2n-1]],{n,20}] (* _Harvey P. Dale_, Jul 19 2018 *)

%o (Haskell)

%o a060381 n = a098012 (2 * n - 1) n  -- _Reinhard Zumkeller_, Oct 02 2014

%o (GAP) P:=Filtered([1..200],IsPrime);;

%o a:=List([1..15],n->Product([0..n-1],k->P[n+k])); # _Muniru A Asiru_, Mar 16 2019

%o (PARI) a(n) = prod(k=n, 2*n-1, prime(k)); \\ _Michel Marcus_, Mar 16 2019

%Y Cf. A002110, A098012.

%Y Related to A006516 via A019565.

%Y A003961, A059896, A306697 are used to express relationship between terms of this sequence.

%K easy,nonn

%O 0,2

%A _Jason Earls_, Apr 03 2001

%E a(0)=1 prepended by _Alois P. Heinz_, Mar 16 2019