A354378 a(n) is the denominator of Sum_{k=0..n} (-1)^k / (2*k)!.

1, 2, 24, 720, 8064, 3628800, 479001600, 87178291200, 20922789888000, 1280474741145600, 2432902008176640000, 1124000727777607680000, 620448401733239439360000, 403291461126605635584000000, 60977668922342772100300800000, 1569543549184562477137920000000

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

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

Example

1, 1/2, 13/24, 389/720, 4357/8064, 1960649/3628800, 258805669/479001600, ...

Mathematica

Table[Sum[(-1)^k/(2 k)!, {k, 0, n}], {n, 0, 15}] // Denominator
nmax = 15; CoefficientList[Series[Cos[Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Denominator

Prog

(PARI) a(n) = denominator(sum(k=0, n, (-1)^k/(2*k)!)); \\ Michel Marcus, May 24 2022

Crossrefs

Cf. A010050, A049470, A053556, A061355, A143383, A354138 (numerators), A354331, A354333, A354335.

Sequence in context: A046977 A309205 A279331 * A119699 A188959 A093459

Adjacent sequences: A354375 A354376 A354377 * A354379 A354380 A354381

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 24 2022

Status

approved