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

1, 2, 3, 3, 12, 24, 252, 56, 18144, 5184, 199584, 33264, 2395008, 48384, 50295168, 100590336, 804722688, 146313216, 137607579648, 6552741888, 11559036690432, 1216740704256, 2924436282679296, 835553223622656, 70186470784303104, 226043384168448, 1895034711176183808

Offset

1,2

Links

Table of n, a(n) for n=1..27.

Formula

a(n) = denominator of A231531(n)/n!. - Chai Wah Wu, Feb 22 2024

Example

See A370551.

Prog

(PARI) a370554(n) = denominator(imag(prod(k=1, n, 1+I/k)))
(Python)
from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
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

Crossrefs

Cf. A231531, A370551, A370552, A370553.

Sequence in context: A303700 A196837 A275212 * A127003 A211673 A184178

Adjacent sequences: A370551 A370552 A370553 * A370555 A370556 A370557

Keyword

nonn,frac,easy

Author

Hugo Pfoertner, Feb 22 2024

Status

approved