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A370554 a(n) is the denominator of the imaginary part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.

%I A370554 #9 Feb 22 2024 17:46:45
%S A370554 1,2,3,3,12,24,252,56,18144,5184,199584,33264,2395008,48384,50295168,
%T A370554 100590336,804722688,146313216,137607579648,6552741888,11559036690432,
%U A370554 1216740704256,2924436282679296,835553223622656,70186470784303104,226043384168448,1895034711176183808
%N A370554 a(n) is the denominator of the imaginary part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.
%F A370554 a(n) = denominator of A231531(n)/n!. - _Chai Wah Wu_, Feb 22 2024
%e A370554 See A370551.
%o A370554 (PARI) a370554(n) = denominator(imag(prod(k=1, n, 1+I/k)))
%o A370554 (Python)
%o A370554 from math import factorial, gcd
%o A370554 from sympy.functions.combinatorial.numbers import stirling
%o A370554 def A370554(n): return (a:=factorial(n))//gcd(a,sum(stirling(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 A370554 Cf. A231531, A370551, A370552, A370553.
%K A370554 nonn,frac,easy
%O A370554 1,2
%A A370554 _Hugo Pfoertner_, Feb 22 2024