A370554 - OEIS

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 #9 Feb 22 2024 17:46:45

%S 1,2,3,3,12,24,252,56,18144,5184,199584,33264,2395008,48384,50295168,

%T 100590336,804722688,146313216,137607579648,6552741888,11559036690432,

%U 1216740704256,2924436282679296,835553223622656,70186470784303104,226043384168448,1895034711176183808

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

%F a(n) = denominator of A231531(n)/n!. - _Chai Wah Wu_, Feb 22 2024

%e See A370551.

%o (PARI) a370554(n) = denominator(imag(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 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 Cf. A231531, A370551, A370552, A370553.

%K nonn,frac,easy

%O 1,2

%A _Hugo Pfoertner_, Feb 22 2024