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A354334
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a(n) is the numerator of Sum_{k=0..n} 1 / (2*k)!.
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5
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1, 3, 37, 1111, 6913, 799933, 739138093, 44841044309, 32285551902481, 9879378882159187, 1251387991740163687, 1734423756551866870183, 136771701945232930334431, 23048564587067030852654113, 42769754577382930342215977687, 409306551305554643375006906464591
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OFFSET
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0,2
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LINKS
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FORMULA
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Numerators of coefficients in expansion of cosh(sqrt(x)) / (1 - x).
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EXAMPLE
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1, 3/2, 37/24, 1111/720, 6913/4480, 799933/518400, 739138093/479001600, ...
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = numerator(sum(k=0, n, 1/(2*k)!)); \\ Michel Marcus, May 24 2022
(Python)
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
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CROSSREFS
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KEYWORD
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nonn,frac,changed
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AUTHOR
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STATUS
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approved
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