A370552 a(n) is the denominator of the real part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.

1, 2, 1, 12, 4, 72, 9, 2016, 2016, 36288, 1512, 2395008, 342144, 33530112, 2095632, 804722688, 12773376, 14485008384, 905313024, 550430318592, 16679706624, 254298807189504, 1177309292544, 3694024778121216, 6380588253118464, 140372941568606208, 2506659670867968

Offset: 1

Author

Hugo Pfoertner, Feb 22 2024

Keywords

• nonn
• frac
• easy

Examples

			See A370551.
		

Crossrefs

Cf. A231530, A370551, A370553, A370554.

Programs

PARI

a370552(n) = denominator(real(prod(k=1, n, 1+I/k)))

Python

from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370552(n): return (a:=factorial(n))//gcd(a,sum(stirling(n+1,(k<<1)+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 A231530(n)/n!. - Chai Wah Wu, Feb 22 2024