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A354333
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a(n) is the denominator of Sum_{k=0..n} (-1)^k / (2*k+1)!.
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5
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1, 6, 120, 5040, 362880, 39916800, 249080832, 1307674368000, 27360571392000, 121645100408832000, 51090942171709440000, 5170403347776995328000, 15511210043330985984000000, 10888869450418352160768000000, 8841761993739701954543616000000, 432780981798838043038187520000000
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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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Denominators of coefficients in expansion of sin(sqrt(x)) / (sqrt(x) * (1 - x)).
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EXAMPLE
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1, 5/6, 101/120, 4241/5040, 305353/362880, 33588829/39916800, 209594293/249080832, ...
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MATHEMATICA
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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
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PROG
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(PARI) a(n) = denominator(sum(k=0, n, (-1)^k/(2*k+1)!)); \\ Michel Marcus, May 24 2022
(Python)
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
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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