A370549 a(n) is the numerator of the imaginary part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.

1, 3, 0, -5, -3, 35, 11, -65, -3055, 4433, 2561, -18863, -614635, 14705, 3871801, -6702403, -23794993, -21392575, 1677354925, 2206770805, -30432904645, -617315066615, 2099373575975, 551582580432325, -11053607615333933, -180184164588301, 4198057769186443, 435884809756010315

Offset: 1

Author

Hugo Pfoertner, Feb 22 2024

Keywords

• frac
• sign
• easy

Examples

			See A370547.
		

Crossrefs

Cf. A105751, A370547, A370548, A370550.

Programs

PARI

a370549(n) = numerator(imag(prod(k=1, n, 1/k+I)))

Python

from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370549(n): return (a:=sum(stirling(n+1,n-(k<<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 A105751(n)/n!. - Chai Wah Wu, Feb 22 2024