cp's OEIS Frontend

A370550 a(n) is the denominator of the imaginary part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.

%I A370550 #9 Feb 22 2024 17:46:09
%S A370550 1,2,1,3,4,24,9,56,2016,5184,1512,33264,342144,48384,2095632,
%T A370550 100590336,12773376,146313216,905313024,6552741888,16679706624,
%U A370550 1216740704256,1177309292544,835553223622656,6380588253118464,226043384168448,2506659670867968,473758677794045952
%N A370550 a(n) is the denominator of the imaginary part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.
%F A370550 a(n) = denominator of A105751(n)/n!. - _Chai Wah Wu_, Feb 22 2024
%e A370550 See A370547.
%o A370550 (PARI) a370550(n) = denominator(imag(prod(k=1, n, 1/k+I)))
%o A370550 (Python)
%o A370550 from math import factorial, gcd
%o A370550 from sympy.functions.combinatorial.numbers import stirling
%o A370550 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 A370550 Cf. A105751, A370547, A370548, A370549.
%K A370550 nonn,frac,easy
%O A370550 1,2
%A A370550 _Hugo Pfoertner_, Feb 22 2024