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a(n) is the numerator of the imaginary part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.
6

%I #9 Feb 22 2024 17:46:26

%S 1,3,0,-5,-3,35,11,-65,-3055,4433,2561,-18863,-614635,14705,3871801,

%T -6702403,-23794993,-21392575,1677354925,2206770805,-30432904645,

%U -617315066615,2099373575975,551582580432325,-11053607615333933,-180184164588301,4198057769186443,435884809756010315

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

%F a(n) = numerator of A105751(n)/n!. - _Chai Wah Wu_, Feb 22 2024

%e See A370547.

%o (PARI) a370549(n) = numerator(imag(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 A370549(n): return (a:=sum(stirling(n+1,n-(k<<1),kind=1)*(-1 if k&1 else 1) for k in range((n>>1)+1)))//gcd(a,factorial(n)) # _Chai Wah Wu_, Feb 22 2024

%Y Cf. A105751, A370547, A370548, A370550.

%K frac,sign,easy

%O 1,2

%A _Hugo Pfoertner_, Feb 22 2024