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A084762
Numerator of Product_{2 <= p < 2*n} (2*n - p)/p.
2
1, 1, 1, 1, 1, 3, 9, 9, 5, 27, 135, 7, 567, 3375, 45, 54675, 1215, 25, 13395375, 168399, 1625, 4975425, 164025, 13125, 5373459, 1031443875, 145775, 2015047125, 5367718125, 931, 377950505625, 644126175, 4501875
OFFSET
1,6
FORMULA
a(n) = numerator( Product_{j=2..A000720(2*n)} (2*n - prime(j))/prime(j) ). - G. C. Greubel, May 16 2023
EXAMPLE
The first terms of a(n)/A084763(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
A084762[n_]:= Numerator[Product[(2*n -Prime[j])/Prime[j], {j, 2, PrimePi[2*n] }]];
Table[A084762[n], {n, 40}] (* G. C. Greubel, May 16 2023 *)
PROG
(Magma)
A084762:= func< n | n eq 1 select 1 else Numerator(&*[(2*n - NthPrime(j))/NthPrime(j): j in [2..#PrimesUpTo(2*n)]]) >;
[A084762(n): n in [1..40]]; // G. C. Greubel, May 16 2023
(SageMath)
def A084762(n): return numerator(product((2*n-j)/j for j in prime_range(3, 2*n) ))
[A084762(n) for n in range(1, 40)] # G. C. Greubel, May 16 2023
CROSSREFS
Cf. A000040, A000720, A084763 (denominators).
Sequence in context: A091559 A268107 A306963 * A188444 A372914 A201409
KEYWORD
nonn,frac
AUTHOR
Reinhard Zumkeller, Jun 03 2003
STATUS
approved