A370551 a(n) is the numerator of the real part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.

1, 1, 0, -5, -3, -73, -11, -2795, -3055, -58643, -2561, -4197973, -614635, -61269445, -3871801, -1495930487, -23794993, -26949145375, -1677354925, -1013112936505, -30432904645, -459074207581145, -2099373575975, -6497000065206625, -11053607615333933, -239235470859971731

Offset: 1

Author

Hugo Pfoertner, Feb 22 2024

Keywords

• sign
• frac
• easy

Examples

			   n  A370551(n)      A370553(n)
           / A370552(n)     / A370554(n)
   1      1/1             +1/1     *i
   2      1/2             +3/2     *i
   3      0/1             +5/3     *i
   4     -5/12            +5/3     *i
   5     -3/4            +19/12    *i
   6    -73/72           +35/24    *i
   7    -11/9           +331/252   *i
   8  -2795/2016         +65/56    *i
   9  -3055/2016      +18265/18144 *i
  10 -58643/36288      +4433/5184  *i
		

Crossrefs

Cf. A231530, A370552, A370553, A370554.

Programs

PARI

a370551(n) = numerator(real(prod(k=1, n, 1+I/k)))

Python

from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370551(n): return (a:=sum(stirling(n+1,(k<<1)+1,kind=1)*(-1 if k&1 else 1) for k in range((n>>1)+1)))//gcd(a,factorial(n)) # Chai Wah Wu, Feb 22 2024

Formula

a(n) = numerator of A231530(n)/n!. - Chai Wah Wu, Feb 22 2024