A370553 a(n) is the numerator of the imaginary part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.

1, 3, 5, 5, 19, 35, 331, 65, 18265, 4433, 141349, 18863, 1035215, 14705, 9158903, 6702403, -34376687, -21392575, -33594289475, -2206770805, -4905856636525, -617315066615, -1713253866399725, -551582580432325, -51270656805872335, -180184164588301, -1630191679256007299

Offset: 1

Author

Hugo Pfoertner, Feb 22 2024

Keywords

• frac
• sign
• easy

Examples

			See A370551.
		

Crossrefs

Cf. A231531, A370551, A370552, A370554.

Programs

PARI

a370553(n) = numerator(imag(prod(k=1, n, 1+I/k)))

Python

from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370553(n): return (a:=sum(stirling(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 A231531(n)/n!. - Chai Wah Wu, Feb 22 2024