A370547 a(n) is the numerator of the real part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.

1, -1, -5, -5, 19, 73, -331, -2795, 18265, 58643, -141349, -4197973, 1035215, 61269445, -9158903, -1495930487, -34376687, 26949145375, 33594289475, -1013112936505, -4905856636525, 459074207581145, 1713253866399725, -6497000065206625, -51270656805872335, 239235470859971731

Offset: 1

Author

Hugo Pfoertner, Feb 22 2024

Keywords

• frac
• sign
• easy

Examples

			   n  a(n)
      A370547(n)      A370549(n)
          / A370548(n)      / A370550(n)
   1     1/1              +1/1     *i
   2    -1/2              +3/2     *i
   3    -5/3              +0/1     *i
   4    -5/12             -5/3     *i
   5    19/12             -3/4     *i
   6    73/72            +35/24    *i
   7  -331/252           +11/9     *i
   8 -2795/2016          -65/56    *i
   9 18265/18144       -3055/2016  *i
  10 58643/36288       +4433/5184  *i
		

Crossrefs

Cf. A105750, A370548, A370549, A370550.

Programs

PARI

a370547(n) = numerator(real(prod(k=1,n,1/k+I)))

Python

from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370547(n): return (a:=sum(stirling(n+1,n+1-(k<<1),kind=1)*(-1 if k&1 else 1) for k in range((n+1>>1)+1)))//gcd(a,factorial(n)) # Chai Wah Wu, Feb 22 2024

Formula

a(n) = numerator of A105750(n)/n!. - Chai Wah Wu, Feb 22 2024