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A370552
a(n) is the denominator of the real part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.
6
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
1,2
FORMULA
a(n) = denominator of A231530(n)/n!. - Chai Wah Wu, Feb 22 2024
EXAMPLE
See A370551.
PROG
(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
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Hugo Pfoertner, Feb 22 2024
STATUS
approved