A090586 Denominator of Sum/Product of first n numbers.

1, 2, 1, 12, 8, 240, 180, 1120, 8064, 725760, 604800, 79833600, 68428800, 830269440, 10897286400, 2615348736000, 2324754432000, 711374856192000, 640237370572800, 11585247657984000, 221172909834240000, 102181884343418880000, 93666727314800640000

Offset

1,2

Comments

a(n) = A000142(n)/A069268(n);

a(p-1) = 2*A000142(p-2) for odd primes.

a(n) = A060593((n - 1)/2) for odd n. - Gregory Gerard Wojnar, Jun 10 2021

Links

Robert Israel, Table of n, a(n) for n = 1..451

Maple

seq(denom((n+1)/(2*(n-1)!)), n=1..25); # Robert Israel, Oct 14 2018

Mathematica

Table[Denominator[(n + 1) / (2 (n - 1)!)], {n, 25}] (* Vincenzo Librandi, Oct 15 2018 *)

Prog

(Magma) [Denominator(n + 1) / (2*Factorial(n - 1)): n in [1..30]]; // Vincenzo Librandi, Oct 15 2018
(Python)
from math import factorial
from sympy import isprime
def A090586(n): return (factorial(n)<<1)//n if n>1 and isprime(n+1) else (factorial(n)<<1)//(n*(n+1)) # Chai Wah Wu, Jun 20 2026

Crossrefs

Cf. A090585 (numerator), A060593.

Main diagonal of A093420.

Sequence in context: A343861 A130559 A135256 * A393943 A268512 A217109

Adjacent sequences: A090583 A090584 A090585 * A090587 A090588 A090589

Keyword

nonn,frac

Author

Reinhard Zumkeller, Dec 03 2003

Status

approved