A354333 a(n) is the denominator of Sum_{k=0..n} (-1)^k / (2*k+1)!.

1, 6, 120, 5040, 362880, 39916800, 249080832, 1307674368000, 27360571392000, 121645100408832000, 51090942171709440000, 5170403347776995328000, 15511210043330985984000000, 10888869450418352160768000000, 8841761993739701954543616000000, 432780981798838043038187520000000

Offset: 0

Author

Ilya Gutkovskiy, May 24 2022

Keywords

• nonn
• frac

Examples

			1, 5/6, 101/120, 4241/5040, 305353/362880, 33588829/39916800, 209594293/249080832, ...
		

Crossrefs

Cf. A009445, A049469, A053556, A061355, A143383, A354299, A354331, A354332 (numerators), A354335.

Programs

Mathematica

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

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

Formula

Denominators of coefficients in expansion of sin(sqrt(x)) / (sqrt(x) * (1 - x)).