A354332
a(n) is the numerator of Sum_{k=0..n} (-1)^k / (2*k+1)!.
Original entry on oeis.org
1, 5, 101, 4241, 305353, 33588829, 209594293, 1100370038249, 23023126954133, 102360822438075317, 42991545423991633141, 4350744396907953273869, 13052233190723859821607001, 9162667699888149594768114701, 7440086172309177470951709137213, 364172638960396581472899447242531
Offset: 0
1, 5/6, 101/120, 4241/5040, 305353/362880, 33588829/39916800, 209594293/249080832, ...
Cf.
A009445,
A049469,
A053557,
A061354,
A103816,
A120265,
A143382,
A354211,
A354298,
A354333 (denominators),
A354334.
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Table[Sum[(-1)^k/(2 k + 1)!, {k, 0, n}], {n, 0, 15}] // Numerator
nmax = 15; CoefficientList[Series[Sin[Sqrt[x]]/(Sqrt[x] (1 - x)), {x, 0, nmax}], x] // Numerator
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a(n) = numerator(sum(k=0, n, (-1)^k/(2*k+1)!)); \\ Michel Marcus, May 24 2022
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from fractions import Fraction
from math import factorial
def A354332(n): return sum(Fraction(-1 if k % 2 else 1,factorial(2*k+1)) for k in range(n+1)).numerator # Chai Wah Wu, May 24 2022
A289381
a(n) = numerator of Sum_{k=1..n} 1/(2*k-1)!!.
Original entry on oeis.org
1, 4, 7, 148, 1333, 4888, 190633, 2859496, 1246447, 923617228, 19395961789, 11438644132, 1013879820791, 301122306774928, 171226409734763, 270708953790660304, 525493851475987649, 104222947209404217052, 11568747140243868092773, 451181138469510855618148
Offset: 1
1, 4/3, 7/5, 148/105, 1333/945, 4888/3465, 190633/135135, 2859496/2027025, 1246447/883575, 923617228/654729075, 19395961789/13749310575, 11438644132/8108567775, ... = a(n)/A289488(n) -> A060196.
A354299
a(n) is the denominator of Sum_{k=1..n} (-1)^(k+1) / (2*k-1)!!.
Original entry on oeis.org
1, 3, 15, 105, 189, 10395, 135135, 2027025, 34459425, 130945815, 13749310575, 316234143225, 7905853580625, 12556355686875, 1238056670725875, 776918153694375, 6332659870762850625, 7642865361265509375, 8200794532637891559375, 63966197354575554163125, 13113070457687988603440625
Offset: 1
1, 2/3, 11/15, 76/105, 137/189, 7534/10395, 97943/135135, 1469144/2027025, 24975449/34459425, ...
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S:= 0: R:= NULL:
for n from 1 to 100 do
S:= S + (-1)^(n+1)/doublefactorial(2*n-1);
R:= R, denom(S);
od:
R; # Robert Israel, Jan 10 2024
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Table[Sum[(-1)^(k + 1)/(2 k - 1)!!, {k, 1, n}], {n, 1, 21}] // Denominator
nmax = 21; CoefficientList[Series[Sqrt[Pi x Exp[-x]/2] Erfi[Sqrt[x/2]]/(1 - x), {x, 0, nmax}], x] // Denominator // Rest
Table[1/(1 + ContinuedFractionK[2 k - 1, 2 k, {k, 1, n - 1}]), {n, 1, 21}] // Denominator
Showing 1-3 of 3 results.