A354211
a(n) is the numerator of Sum_{k=0..n} 1 / (2*k+1)!.
Original entry on oeis.org
1, 7, 47, 5923, 426457, 15636757, 7318002277, 1536780478171, 603180793741, 142957467201379447, 60042136224579367741, 10127106976545720025649, 18228792557782296046168201, 12796612375563171824410077103, 3463616416319098507140327535879, 1380498543075754976417359117871773
Offset: 0
1, 7/6, 47/40, 5923/5040, 426457/362880, 15636757/13305600, 7318002277/6227020800, ...
Cf.
A009445,
A053557,
A061354,
A073742,
A103816,
A120265,
A143382,
A289381,
A354331 (denominators),
A354332,
A354334.
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Table[Sum[1/(2 k + 1)!, {k, 0, n}], {n, 0, 15}] // Numerator
nmax = 15; CoefficientList[Series[Sinh[Sqrt[x]]/(Sqrt[x] (1 - x)), {x, 0, nmax}], x] // Numerator
-
a(n) = numerator(sum(k=0, n, 1/(2*k+1)!)); \\ Michel Marcus, May 24 2022
-
from fractions import Fraction
from math import factorial
def A354211(n): return sum(Fraction(1,factorial(2*k+1)) for k in range(n+1)).numerator # Chai Wah Wu, May 24 2022
A354333
a(n) is the denominator of Sum_{k=0..n} (-1)^k / (2*k+1)!.
Original entry on oeis.org
1, 6, 120, 5040, 362880, 39916800, 249080832, 1307674368000, 27360571392000, 121645100408832000, 51090942171709440000, 5170403347776995328000, 15511210043330985984000000, 10888869450418352160768000000, 8841761993739701954543616000000, 432780981798838043038187520000000
Offset: 0
1, 5/6, 101/120, 4241/5040, 305353/362880, 33588829/39916800, 209594293/249080832, ...
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Table[Sum[(-1)^k/(2 k + 1)!, {k, 0, n}], {n, 0, 15}] // Denominator
nmax = 15; CoefficientList[Series[Sin[Sqrt[x]]/(Sqrt[x] (1 - x)), {x, 0, nmax}], x] // Denominator
-
a(n) = denominator(sum(k=0, n, (-1)^k/(2*k+1)!)); \\ Michel Marcus, May 24 2022
-
from fractions import Fraction
from math import factorial
def A354333(n): return sum(Fraction(-1 if k % 2 else 1,factorial(2*k+1)) for k in range(n+1)).denominator # Chai Wah Wu, May 24 2022
A354335
a(n) is the denominator of Sum_{k=0..n} 1 / (2*k)!.
Original entry on oeis.org
1, 2, 24, 720, 4480, 518400, 479001600, 29059430400, 20922789888000, 6402373705728000, 810967336058880000, 1124000727777607680000, 88635485961891348480000, 14936720782466875392000000, 27717122237428532772864000000, 265252859812191058636308480000000
Offset: 0
1, 3/2, 37/24, 1111/720, 6913/4480, 799933/518400, 739138093/479001600, ...
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Table[Sum[1/(2 k)!, {k, 0, n}], {n, 0, 15}] // Denominator
nmax = 15; CoefficientList[Series[Cosh[Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Denominator
-
a(n) = denominator(sum(k=0, n, 1/(2*k)!)); \\ Michel Marcus, May 24 2022
-
from fractions import Fraction
from math import factorial
def A354335(n): return sum(Fraction(1,factorial(2*k)) for k in range(n+1)).denominator # Chai Wah Wu, May 24 2022
A354378
a(n) is the denominator of Sum_{k=0..n} (-1)^k / (2*k)!.
Original entry on oeis.org
1, 2, 24, 720, 8064, 3628800, 479001600, 87178291200, 20922789888000, 1280474741145600, 2432902008176640000, 1124000727777607680000, 620448401733239439360000, 403291461126605635584000000, 60977668922342772100300800000, 1569543549184562477137920000000
Offset: 0
1, 1/2, 13/24, 389/720, 4357/8064, 1960649/3628800, 258805669/479001600, ...
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Table[Sum[(-1)^k/(2 k)!, {k, 0, n}], {n, 0, 15}] // Denominator
nmax = 15; CoefficientList[Series[Cos[Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Denominator
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a(n) = denominator(sum(k=0, n, (-1)^k/(2*k)!)); \\ Michel Marcus, May 24 2022
Showing 1-4 of 4 results.