A370548 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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