A354335 a(n) is the denominator of Sum_{k=0..n} 1 / (2*k)!.

1, 2, 24, 720, 4480, 518400, 479001600, 29059430400, 20922789888000, 6402373705728000, 810967336058880000, 1124000727777607680000, 88635485961891348480000, 14936720782466875392000000, 27717122237428532772864000000, 265252859812191058636308480000000

Offset

0,2

Links

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

Formula

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

Example

1, 3/2, 37/24, 1111/720, 6913/4480, 799933/518400, 739138093/479001600, ...

Mathematica

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

Prog

(PARI) a(n) = denominator(sum(k=0, n, 1/(2*k)!)); \\ Michel Marcus, May 24 2022
(Python)
from fractions import Fraction
from math import factorial
def A354335(n): return sum(Fraction(1, factorial(2*k)) for k in range(n+1)).denominator # Chai Wah Wu, May 24 2022

Crossrefs

Cf. A010050, A053556, A061355, A073743, A143383, A354331, A354333, A354334 (numerators).

Sequence in context: A009750 A030438 A012723 * A069150 A323491 A046977

Adjacent sequences: A354332 A354333 A354334 * A354336 A354337 A354338

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 24 2022

Status

approved