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a(n) is the denominator of the imaginary part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.
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%I #9 Feb 22 2024 17:46:09

%S 1,2,1,3,4,24,9,56,2016,5184,1512,33264,342144,48384,2095632,

%T 100590336,12773376,146313216,905313024,6552741888,16679706624,

%U 1216740704256,1177309292544,835553223622656,6380588253118464,226043384168448,2506659670867968,473758677794045952

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

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

%e See A370547.

%o (PARI) a370550(n) = denominator(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 A370550(n): return (a:=factorial(n))//gcd(a,sum(stirling(n+1,n-(k<<1),kind=1)*(-1 if k&1 else 1) for k in range((n>>1)+1))) # _Chai Wah Wu_, Feb 22 2024

%Y Cf. A105751, A370547, A370548, A370549.

%K nonn,frac,easy

%O 1,2

%A _Hugo Pfoertner_, Feb 22 2024