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A370552 a(n) is the denominator of the real part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.

%I A370552 #11 Feb 23 2024 01:45:37
%S A370552 1,2,1,12,4,72,9,2016,2016,36288,1512,2395008,342144,33530112,2095632,
%T A370552 804722688,12773376,14485008384,905313024,550430318592,16679706624,
%U A370552 254298807189504,1177309292544,3694024778121216,6380588253118464,140372941568606208,2506659670867968
%N A370552 a(n) is the denominator of the real part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.
%F A370552 a(n) = denominator of A231530(n)/n!. - _Chai Wah Wu_, Feb 22 2024
%e A370552 See A370551.
%o A370552 (PARI) a370552(n) = denominator(real(prod(k=1, n, 1+I/k)))
%o A370552 (Python)
%o A370552 from math import factorial, gcd
%o A370552 from sympy.functions.combinatorial.numbers import stirling
%o A370552 def A370552(n): return (a:=factorial(n))//gcd(a,sum(stirling(n+1,(k<<1)+1,kind=1)*(-1 if k&1 else 1) for k in range((n>>1)+1))) # _Chai Wah Wu_, Feb 22 2024
%Y A370552 Cf. A231530, A370551, A370553, A370554.
%K A370552 nonn,frac,easy
%O A370552 1,2
%A A370552 _Hugo Pfoertner_, Feb 22 2024