A060381 a(n) = prime(n)*prime(n+1)*...*prime(2*n-1), where prime(i) is the i-th prime.

1, 2, 15, 385, 17017, 1062347, 86822723, 10131543907, 1204461778591, 198229051666003, 35224440615606707, 6295457783127226289, 1331590860773071702483, 310692537866322378582047, 78832548083496383033878901, 21381953681344611984282084241

Offset: 0

Author

Jason Earls, Apr 03 2001

Keywords

• easy
• nonn

Comments

Central terms of triangle A098012. - Reinhard Zumkeller, Oct 02 2014

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

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A002110, A098012.

Related to A006516 via A019565.

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

Programs

GAP

P:=Filtered([1..200],IsPrime);;
a:=List([1..15],n->Product([0..n-1],k->P[n+k])); # Muniru A Asiru, Mar 16 2019

Haskell

a060381 n = a098012 (2 * n - 1) n  -- Reinhard Zumkeller, Oct 02 2014

Maple

seq(mul(ithprime(n+k),k=0..n-1),n=0..15); # Muniru A Asiru, Mar 16 2019

Mathematica

Table[Times@@Prime[Range[n,2n-1]],{n,20}] (* Harvey P. Dale, Jul 19 2018 *)

PARI

a(n) = prod(k=n, 2*n-1, prime(k)); \\ Michel Marcus, Mar 16 2019

Formula

a(n) = A002110(2*n-1)/A002110(n-1). - Michel Marcus, Mar 16 2019

From Peter Munn, Feb 18 2020: (Start)

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

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

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

(End)

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 16 2019