A354331
a(n) is the denominator of Sum_{k=0..n} 1 / (2*k+1)!.
Original entry on oeis.org
1, 6, 40, 5040, 362880, 13305600, 6227020800, 1307674368000, 513257472000, 121645100408832000, 51090942171709440000, 8617338912961658880000, 15511210043330985984000000, 10888869450418352160768000000, 2947253997913233984847872000000, 1174691236311131831103651840000000
Offset: 0
1, 7/6, 47/40, 5923/5040, 426457/362880, 15636757/13305600, 7318002277/6227020800, ...
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Table[Sum[1/(2 k + 1)!, {k, 0, n}], {n, 0, 15}] // Denominator
nmax = 15; CoefficientList[Series[Sinh[Sqrt[x]]/(Sqrt[x] (1 - x)), {x, 0, nmax}], x] // Denominator
-
a(n) = denominator(sum(k=0, n, 1/(2*k+1)!)); \\ Michel Marcus, May 24 2022
-
from fractions import Fraction
from math import factorial
def A354331(n): return sum(Fraction(1,factorial(2*k+1)) for k in range(n+1)).denominator # Chai Wah Wu, May 24 2022
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
-
a(n) = numerator(sum(k=0, n, (-1)^k/(2*k+1)!)); \\ Michel Marcus, May 24 2022
-
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
A354334
a(n) is the numerator of Sum_{k=0..n} 1 / (2*k)!.
Original entry on oeis.org
1, 3, 37, 1111, 6913, 799933, 739138093, 44841044309, 32285551902481, 9879378882159187, 1251387991740163687, 1734423756551866870183, 136771701945232930334431, 23048564587067030852654113, 42769754577382930342215977687, 409306551305554643375006906464591
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}] // Numerator
nmax = 15; CoefficientList[Series[Cosh[Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Numerator
Accumulate[1/(2*Range[0,20])!]//Numerator (* Harvey P. Dale, Sep 05 2024 *)
-
a(n) = numerator(sum(k=0, n, 1/(2*k)!)); \\ Michel Marcus, May 24 2022
-
from fractions import Fraction
from math import factorial
def A354334(n): return sum(Fraction(1,factorial(2*k)) for k in range(n+1)).numerator # Chai Wah Wu, May 24 2022
A354138
a(n) is the numerator of Sum_{k=0..n} (-1)^k / (2*k)!.
Original entry on oeis.org
1, 1, 13, 389, 4357, 1960649, 258805669, 47102631757, 11304631621681, 691843455246877, 1314502564969066301, 607300185015708631061, 335229702128671164345673, 217899306383636256824687449, 32946375125205802031892742289, 848027998784883070051677094421
Offset: 0
1, 1/2, 13/24, 389/720, 4357/8064, 1960649/3628800, 258805669/479001600, ...
Cf.
A010050,
A049470,
A053557,
A061354,
A103816,
A120265,
A143382,
A354211,
A354332,
A354334,
A354378 (denominators).
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Table[Sum[(-1)^k/(2 k)!, {k, 0, n}], {n, 0, 15}] // Numerator
nmax = 15; CoefficientList[Series[Cos[Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Numerator
-
a(n) = numerator(sum(k=0, n, (-1)^k/(2*k)!)); \\ Michel Marcus, May 24 2022
Showing 1-4 of 4 results.