A261130 a(n) = Product(p prime | n < p <= 2*n).

1, 2, 3, 5, 35, 7, 77, 143, 143, 2431, 46189, 4199, 96577, 7429, 7429, 215441, 6678671, 392863, 392863, 765049, 765049, 31367009, 1348781387, 58642669, 2756205443, 2756205443, 2756205443, 146078888479, 146078888479, 5037203051, 297194980009, 584803025179

Offset

0,2

Comments

Essentially the same as A068111. - R. J. Mathar, Nov 23 2015

a(n) is a divisor of binomial(2*n, n); the quotient binomial(2*n, n) / a(n) is A263931(n). - Robert FERREOL, Sep 03 2022

Links

Table of n, a(n) for n=0..31.

Example

a(0) = 1 because the empty product is 1 by convention.
a(4) = 35 because {p prime | 4 < p <= 8} = {5, 7}.

Maple

a := n -> convert(select(isprime, {$n+1..2*n}), `*`):
print(seq(a(n), n=0..31));

Mathematica

Join[{1}, Table[Times@@Prime[Range[PrimePi[n]+1, PrimePi[2n]]], {n, 40}]] (* Harvey P. Dale, May 09 2017 *)

Prog

(PARI) A261130(n, P=1)={forprime(p=n+1, 2*n, P*=p); P} \\ M. F. Hasler, Nov 25 2015
(Python)
from sympy import primorial
def A261130(n): return primorial(n<<1, nth=False)//primorial(n, nth=False) if n else 1 # Chai Wah Wu, Sep 07 2022

Crossrefs

Cf. A000984 (binomial(2*n,n)), A034386, A263931, A356637.

Sequence in context: A041019 A041977 A362640 * A271387 A089213 A029499

Adjacent sequences: A261127 A261128 A261129 * A261131 A261132 A261133

Keyword

nonn,easy

Author

Peter Luschny, Oct 31 2015

Status

approved