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%I #31 Sep 07 2022 15:49:18
%S 1,2,3,5,35,7,77,143,143,2431,46189,4199,96577,7429,7429,215441,
%T 6678671,392863,392863,765049,765049,31367009,1348781387,58642669,
%U 2756205443,2756205443,2756205443,146078888479,146078888479,5037203051,297194980009,584803025179
%N a(n) = Product(p prime | n < p <= 2*n).
%C Essentially the same as A068111. - _R. J. Mathar_, Nov 23 2015
%C 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
%e a(0) = 1 because the empty product is 1 by convention.
%e a(4) = 35 because {p prime | 4 < p <= 8} = {5, 7}.
%p a := n -> convert(select(isprime, {$n+1..2*n}),`*`):
%p print(seq(a(n), n=0..31));
%t Join[{1},Table[Times@@Prime[Range[PrimePi[n]+1,PrimePi[2n]]],{n,40}]] (* _Harvey P. Dale_, May 09 2017 *)
%o (PARI) A261130(n,P=1)={forprime(p=n+1,2*n,P*=p);P} \\ _M. F. Hasler_, Nov 25 2015
%o (Python)
%o from sympy import primorial
%o def A261130(n): return primorial(n<<1,nth=False)//primorial(n,nth=False) if n else 1 # _Chai Wah Wu_, Sep 07 2022
%Y Cf. A000984 (binomial(2*n,n)), A034386, A263931, A356637.
%K nonn,easy
%O 0,2
%A _Peter Luschny_, Oct 31 2015
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