A370554 a(n) is the denominator of the imaginary part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.

1, 2, 3, 3, 12, 24, 252, 56, 18144, 5184, 199584, 33264, 2395008, 48384, 50295168, 100590336, 804722688, 146313216, 137607579648, 6552741888, 11559036690432, 1216740704256, 2924436282679296, 835553223622656, 70186470784303104, 226043384168448, 1895034711176183808

Offset: 1

Author

Hugo Pfoertner, Feb 22 2024

Keywords

• nonn
• frac
• easy

Examples

			See A370551.
		

Crossrefs

Cf. A231531, A370551, A370552, A370553.

Programs

PARI

a370554(n) = denominator(imag(prod(k=1, n, 1+I/k)))

Python

from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370554(n): return (a:=factorial(n))//gcd(a,sum(stirling(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 A231531(n)/n!. - Chai Wah Wu, Feb 22 2024