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A370547 a(n) is the numerator of the real part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.

%I A370547 #17 Feb 22 2024 17:46:22
%S A370547 1,-1,-5,-5,19,73,-331,-2795,18265,58643,-141349,-4197973,1035215,
%T A370547 61269445,-9158903,-1495930487,-34376687,26949145375,33594289475,
%U A370547 -1013112936505,-4905856636525,459074207581145,1713253866399725,-6497000065206625,-51270656805872335,239235470859971731
%N A370547 a(n) is the numerator of the real part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.
%F A370547 a(n) = numerator of A105750(n)/n!. - _Chai Wah Wu_, Feb 22 2024
%e A370547    n  a(n)
%e A370547       A370547(n)      A370549(n)
%e A370547           / A370548(n)      / A370550(n)
%e A370547    1     1/1              +1/1     *i
%e A370547    2    -1/2              +3/2     *i
%e A370547    3    -5/3              +0/1     *i
%e A370547    4    -5/12             -5/3     *i
%e A370547    5    19/12             -3/4     *i
%e A370547    6    73/72            +35/24    *i
%e A370547    7  -331/252           +11/9     *i
%e A370547    8 -2795/2016          -65/56    *i
%e A370547    9 18265/18144       -3055/2016  *i
%e A370547   10 58643/36288       +4433/5184  *i
%o A370547 (PARI) a370547(n) = numerator(real(prod(k=1,n,1/k+I)))
%o A370547 (Python)
%o A370547 from math import factorial, gcd
%o A370547 from sympy.functions.combinatorial.numbers import stirling
%o A370547 def A370547(n): return (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)))//gcd(a,factorial(n)) # _Chai Wah Wu_, Feb 22 2024
%Y A370547 Cf. A105750, A370548, A370549, A370550.
%K A370547 frac,sign,easy
%O A370547 1,3
%A A370547 _Hugo Pfoertner_, Feb 22 2024