A354211 a(n) is the numerator of Sum_{k=0..n} 1 / (2*k+1)!.

1, 7, 47, 5923, 426457, 15636757, 7318002277, 1536780478171, 603180793741, 142957467201379447, 60042136224579367741, 10127106976545720025649, 18228792557782296046168201, 12796612375563171824410077103, 3463616416319098507140327535879, 1380498543075754976417359117871773

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, A053557, A061354, A073742, A103816, A120265, A143382, A289381, A354331 (denominators), A354332, A354334.

Programs

Mathematica

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

PARI

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

Python

from fractions import Fraction
from math import factorial
def A354211(n): return sum(Fraction(1,factorial(2*k+1)) for k in range(n+1)).numerator # Chai Wah Wu, May 24 2022

Formula

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