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

0,2

Links

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

Formula

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

Example

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

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

Prog

(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

Crossrefs

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

Sequence in context: A086803 A136382 A096716 * A000611 A043069 A257602

Adjacent sequences: A354328 A354329 A354330 * A354332 A354333 A354334

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 24 2022

Status

approved