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A370550
a(n) is the denominator of the imaginary part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.
6
1, 2, 1, 3, 4, 24, 9, 56, 2016, 5184, 1512, 33264, 342144, 48384, 2095632, 100590336, 12773376, 146313216, 905313024, 6552741888, 16679706624, 1216740704256, 1177309292544, 835553223622656, 6380588253118464, 226043384168448, 2506659670867968, 473758677794045952
OFFSET
1,2
FORMULA
a(n) = denominator of A105751(n)/n!. - Chai Wah Wu, Feb 22 2024
EXAMPLE
See A370547.
PROG
(PARI) a370550(n) = denominator(imag(prod(k=1, n, 1/k+I)))
(Python)
from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370550(n): return (a:=factorial(n))//gcd(a, sum(stirling(n+1, n-(k<<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