A354331 a(n) is the denominator of Sum_{k=0..n} 1 / (2*k+1)!.

1, 6, 40, 5040, 362880, 13305600, 6227020800, 1307674368000, 513257472000, 121645100408832000, 51090942171709440000, 8617338912961658880000, 15511210043330985984000000, 10888869450418352160768000000, 2947253997913233984847872000000, 1174691236311131831103651840000000

Offset: 0

Author

Ilya Gutkovskiy, May 24 2022

Keywords

• nonn
• frac

Examples

			1, 7/6, 47/40, 5923/5040, 426457/362880, 15636757/13305600, 7318002277/6227020800, ...
		

Crossrefs

Cf. A009445, A053556, A061355, A073742, A143383, A289488, A354211 (numerators), A354333, A354335.

Programs

Mathematica

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

PARI

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

Python

from fractions import Fraction
from math import factorial
def A354331(n): return sum(Fraction(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 sinh(sqrt(x)) / (sqrt(x) * (1 - x)).