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