A370548 a(n) is the denominator of the real part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.

1, 2, 3, 12, 12, 72, 252, 2016, 18144, 36288, 199584, 2395008, 2395008, 33530112, 50295168, 804722688, 804722688, 14485008384, 137607579648, 550430318592, 11559036690432, 254298807189504, 2924436282679296, 3694024778121216, 70186470784303104, 140372941568606208

Offset: 1

Author

Hugo Pfoertner, Feb 22 2024

Keywords

• nonn
• frac
• easy

Examples

			See A370547.
		

Crossrefs

Cf. A105750, A370547, A370549, A370550.

Programs

PARI

a370548(n) = denominator(real(prod(k=1, n, 1/k+I)))

Python

from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370548(n): return (a:=factorial(n))//gcd(a,sum(stirling(n+1,n+1-(k<<1),kind=1)*(-1 if k&1 else 1) for k in range((n+1>>1)+1))) # Chai Wah Wu, Feb 22 2024

Formula

a(n) = denominator of A105750(n)/n!. - Chai Wah Wu, Feb 22 2024