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A370547
a(n) is the numerator of the real part of Product_{k=1..n} (1/k + i) where i is the imaginary unit.
6
1, -1, -5, -5, 19, 73, -331, -2795, 18265, 58643, -141349, -4197973, 1035215, 61269445, -9158903, -1495930487, -34376687, 26949145375, 33594289475, -1013112936505, -4905856636525, 459074207581145, 1713253866399725, -6497000065206625, -51270656805872335, 239235470859971731
OFFSET
1,3
FORMULA
a(n) = numerator of A105750(n)/n!. - Chai Wah Wu, Feb 22 2024
EXAMPLE
n a(n)
/ A370548(n) / A370550(n)
1 1/1 +1/1 *i
2 -1/2 +3/2 *i
3 -5/3 +0/1 *i
4 -5/12 -5/3 *i
5 19/12 -3/4 *i
6 73/72 +35/24 *i
7 -331/252 +11/9 *i
8 -2795/2016 -65/56 *i
9 18265/18144 -3055/2016 *i
10 58643/36288 +4433/5184 *i
PROG
(PARI) a370547(n) = numerator(real(prod(k=1, n, 1/k+I)))
(Python)
from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370547(n): return (a:=sum(stirling(n+1, n+1-(k<<1), kind=1)*(-1 if k&1 else 1) for k in range((n+1>>1)+1)))//gcd(a, factorial(n)) # Chai Wah Wu, Feb 22 2024
CROSSREFS
KEYWORD
frac,sign,easy
AUTHOR
Hugo Pfoertner, Feb 22 2024
STATUS
approved