A370550 a(n) is the denominator of the imaginary part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.

1, 2, 1, 3, 4, 24, 9, 56, 2016, 5184, 1512, 33264, 342144, 48384, 2095632, 100590336, 12773376, 146313216, 905313024, 6552741888, 16679706624, 1216740704256, 1177309292544, 835553223622656, 6380588253118464, 226043384168448, 2506659670867968, 473758677794045952

Offset: 1

Author

Hugo Pfoertner, Feb 22 2024

Keywords

• nonn
• frac
• easy

Examples

			See A370547.
		

Crossrefs

Cf. A105751, A370547, A370548, A370549.

Programs

PARI

a370550(n) = denominator(imag(prod(k=1, n, 1/k+I)))

Python

from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370550(n): return (a:=factorial(n))//gcd(a,sum(stirling(n+1,n-(k<<1),kind=1)*(-1 if k&1 else 1) for k in range((n>>1)+1))) # Chai Wah Wu, Feb 22 2024

Formula

a(n) = denominator of A105751(n)/n!. - Chai Wah Wu, Feb 22 2024