A370551
a(n) is the numerator of the real part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.
Original entry on oeis.org
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
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
-
a370551(n) = numerator(real(prod(k=1, n, 1+I/k)))
-
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
A370553
a(n) is the numerator of the imaginary part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.
Original entry on oeis.org
1, 3, 5, 5, 19, 35, 331, 65, 18265, 4433, 141349, 18863, 1035215, 14705, 9158903, 6702403, -34376687, -21392575, -33594289475, -2206770805, -4905856636525, -617315066615, -1713253866399725, -551582580432325, -51270656805872335, -180184164588301, -1630191679256007299
Offset: 1
-
a370553(n) = numerator(imag(prod(k=1, n, 1+I/k)))
-
from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370553(n): return (a:=sum(stirling(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
A370554
a(n) is the denominator of the imaginary part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.
Original entry on oeis.org
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
-
a370554(n) = denominator(imag(prod(k=1, n, 1+I/k)))
-
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
A370555
a(n) is the numerator of f(n)*conj(f(n)), where f(n) = Product_{k=1..n} (1/k + i), i is the imaginary unit, and conj(z) is the complex conjugate of z.
Original entry on oeis.org
2, 5, 25, 425, 221, 8177, 204425, 13287625, 544792625, 2200962205, 134258694505, 19467510703225, 9791351537125, 1928896252813625, 8718611062717585, 2240683043118419345, 1124218135820660225, 365370894141714573125, 66132131839650337735625, 1060759394707991417279425
Offset: 1
A370556 are the corresponding denominators.
A370556
a(n) is the denominator of f(n)*conj(f(n)), where f(n) = Product_{k=1..n} (1/k + i), i is the imaginary unit, and conj(z) is the complex conjugate of z.
Original entry on oeis.org
1, 2, 9, 144, 72, 2592, 63504, 4064256, 164602368, 658409472, 39833773056, 5736063320064, 2868031660032, 562134205366272, 2529603924148224, 647578604581945344, 323789302290972672, 104907733942275145728, 18935845976580663803904, 302973535625290620862464, 66805664605376581900173312
Offset: 1
A370555 are the corresponding numerators.
Showing 1-5 of 5 results.
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