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A370551 a(n) is the numerator of the real part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.

%I A370551 #11 Feb 22 2024 17:46:30
%S A370551 1,1,0,-5,-3,-73,-11,-2795,-3055,-58643,-2561,-4197973,-614635,
%T A370551 -61269445,-3871801,-1495930487,-23794993,-26949145375,-1677354925,
%U A370551 -1013112936505,-30432904645,-459074207581145,-2099373575975,-6497000065206625,-11053607615333933,-239235470859971731
%N A370551 a(n) is the numerator of the real part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.
%F A370551 a(n) = numerator of A231530(n)/n!. - _Chai Wah Wu_, Feb 22 2024
%e A370551    n  A370551(n)      A370553(n)
%e A370551            / A370552(n)     / A370554(n)
%e A370551    1      1/1             +1/1     *i
%e A370551    2      1/2             +3/2     *i
%e A370551    3      0/1             +5/3     *i
%e A370551    4     -5/12            +5/3     *i
%e A370551    5     -3/4            +19/12    *i
%e A370551    6    -73/72           +35/24    *i
%e A370551    7    -11/9           +331/252   *i
%e A370551    8  -2795/2016         +65/56    *i
%e A370551    9  -3055/2016      +18265/18144 *i
%e A370551   10 -58643/36288      +4433/5184  *i
%o A370551 (PARI) a370551(n) = numerator(real(prod(k=1, n, 1+I/k)))
%o A370551 (Python)
%o A370551 from math import factorial, gcd
%o A370551 from sympy.functions.combinatorial.numbers import stirling
%o A370551 def A370551(n): return (a:=sum(stirling(n+1,(k<<1)+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 A370551 Cf. A231530, A370552, A370553, A370554.
%K A370551 sign,frac,easy
%O A370551 1,4
%A A370551 _Hugo Pfoertner_, Feb 22 2024