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URL: https://oeis.org/A060381

⇱ A060381 - OEIS

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A060381
a(n) = prime(n)*prime(n+1)*...*prime(2*n-1), where prime(i) is the i-th prime.
3
1, 2, 15, 385, 17017, 1062347, 86822723, 10131543907, 1204461778591, 198229051666003, 35224440615606707, 6295457783127226289, 1331590860773071702483, 310692537866322378582047, 78832548083496383033878901, 21381953681344611984282084241
OFFSET
0,2
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
LINKS
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)
EXAMPLE
a(1)=2; a(2) = 3*5 = 15; a(3) = 5*7*11 = 385.
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 *)
PROG
(Haskell)
a060381 n = a098012 (2 * n - 1) n -- Reinhard Zumkeller, Oct 02 2014
(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
(PARI) a(n) = prod(k=n, 2*n-1, prime(k)); \\ Michel Marcus, Mar 16 2019
CROSSREFS
Related to A006516 via A019565.
A003961, A059896, A306697 are used to express relationship between terms of this sequence.
Sequence in context: A254224 A071102 A272899 * A256369 A145328 A139810
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Apr 03 2001
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Mar 16 2019
STATUS
approved