A370552 - OEIS

%I #11 Feb 23 2024 01:45:37

%S 1,2,1,12,4,72,9,2016,2016,36288,1512,2395008,342144,33530112,2095632,

%T 804722688,12773376,14485008384,905313024,550430318592,16679706624,

%U 254298807189504,1177309292544,3694024778121216,6380588253118464,140372941568606208,2506659670867968

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

%F a(n) = denominator of A231530(n)/n!. - _Chai Wah Wu_, Feb 22 2024

%e See A370551.

%o (PARI) a370552(n) = denominator(real(prod(k=1, n, 1+I/k)))

%o (Python)

%o from math import factorial, gcd

%o from sympy.functions.combinatorial.numbers import stirling

%o 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 Cf. A231530, A370551, A370553, A370554.

%K nonn,frac,easy

%O 1,2

%A _Hugo Pfoertner_, Feb 22 2024