A370552 a(n) is the denominator of the real part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.

1, 2, 1, 12, 4, 72, 9, 2016, 2016, 36288, 1512, 2395008, 342144, 33530112, 2095632, 804722688, 12773376, 14485008384, 905313024, 550430318592, 16679706624, 254298807189504, 1177309292544, 3694024778121216, 6380588253118464, 140372941568606208, 2506659670867968

Offset

1,2

Links

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

Formula

a(n) = denominator of A231530(n)/n!. - Chai Wah Wu, Feb 22 2024

Example

See A370551.

Prog

(PARI) a370552(n) = denominator(real(prod(k=1, n, 1+I/k)))
(Python)
from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
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

Crossrefs

Cf. A231530, A370551, A370553, A370554.

Sequence in context: A288359 A107722 A357013 * A167128 A332749 A342430

Adjacent sequences: A370549 A370550 A370551 * A370553 A370554 A370555

Keyword

nonn,frac,easy

Author

Hugo Pfoertner, Feb 22 2024

Status

approved