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A370551
a(n) is the numerator of the real part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.
6
1, 1, 0, -5, -3, -73, -11, -2795, -3055, -58643, -2561, -4197973, -614635, -61269445, -3871801, -1495930487, -23794993, -26949145375, -1677354925, -1013112936505, -30432904645, -459074207581145, -2099373575975, -6497000065206625, -11053607615333933, -239235470859971731
OFFSET
1,4
FORMULA
a(n) = numerator of A231530(n)/n!. - Chai Wah Wu, Feb 22 2024
EXAMPLE
n A370551(n) A370553(n)
/ A370552(n) / A370554(n)
1 1/1 +1/1 *i
2 1/2 +3/2 *i
3 0/1 +5/3 *i
4 -5/12 +5/3 *i
5 -3/4 +19/12 *i
6 -73/72 +35/24 *i
7 -11/9 +331/252 *i
8 -2795/2016 +65/56 *i
9 -3055/2016 +18265/18144 *i
10 -58643/36288 +4433/5184 *i
PROG
(PARI) a370551(n) = numerator(real(prod(k=1, n, 1+I/k)))
(Python)
from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370551(n): return (a:=sum(stirling(n+1, (k<<1)+1, kind=1)*(-1 if k&1 else 1) for k in range((n>>1)+1)))//gcd(a, factorial(n)) # Chai Wah Wu, Feb 22 2024
CROSSREFS
KEYWORD
sign,frac,easy
AUTHOR
Hugo Pfoertner, Feb 22 2024
STATUS
approved