OFFSET
1,2
LINKS
FORMULA
a(n) = denominator( Product_{j=2..A000720(2*n)} (2*n - prime(j) ) / prime(j) ). - G. C. Greubel, May 16 2023
EXAMPLE
The first terms of A084762(n)/a(n): 1/1, 1/3, 1/5, 1/7, 1/1, 3/11, 9/65, 9/7, 5/17, 27/209, 135/91, 7/23, ...
MATHEMATICA
A084763[n_]:= Denominator[Product[(2*n -Prime[j])/Prime[j], {j, 2, PrimePi[2*n] }]];
Table[A084763[n], {n, 40}] (* G. C. Greubel, May 16 2023 *)
PROG
(Magma)
A084763:= func< n | n eq 1 select 1 else Denominator(&*[(2*n - NthPrime(j))/NthPrime(j): j in [2..#PrimesUpTo(2*n)]]) >;
[A084763(n): n in [1..40]]; // G. C. Greubel, May 16 2023
(SageMath)
def A084763(n): return denominator(product((2*n-j)/j for j in prime_range(3, 2*n)))
[A084763(n) for n in range(1, 40)] # G. C. Greubel, May 16 2023
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Reinhard Zumkeller, Jun 03 2003
STATUS
approved