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A370548 a(n) is the denominator of the real part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.

%I A370548 #13 Feb 22 2024 17:46:14
%S A370548 1,2,3,12,12,72,252,2016,18144,36288,199584,2395008,2395008,33530112,
%T A370548 50295168,804722688,804722688,14485008384,137607579648,550430318592,
%U A370548 11559036690432,254298807189504,2924436282679296,3694024778121216,70186470784303104,140372941568606208
%N A370548 a(n) is the denominator of the real part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.
%F A370548 a(n) = denominator of A105750(n)/n!. - _Chai Wah Wu_, Feb 22 2024
%e A370548 See A370547.
%o A370548 (PARI) a370548(n) = denominator(real(prod(k=1, n, 1/k+I)))
%o A370548 (Python)
%o A370548 from math import factorial, gcd
%o A370548 from sympy.functions.combinatorial.numbers import stirling
%o A370548 def A370548(n): return (a:=factorial(n))//gcd(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))) # _Chai Wah Wu_, Feb 22 2024
%Y A370548 Cf. A105750, A370547, A370549, A370550.
%K A370548 nonn,frac,easy
%O A370548 1,2
%A A370548 _Hugo Pfoertner_, Feb 22 2024