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

1,2

Links

Table of n, a(n) for n=1..26.

Formula

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

Example

See A370547.

Prog

(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

Crossrefs

Cf. A105750, A370547, A370549, A370550.

Sequence in context: A002944 A266366 A201501 * A302843 A037321 A227745

Adjacent sequences: A370545 A370546 A370547 * A370549 A370550 A370551

Keyword

nonn,frac,easy

Author

Hugo Pfoertner, Feb 22 2024

Status

approved