A354334 a(n) is the numerator of Sum_{k=0..n} 1 / (2*k)!.

1, 3, 37, 1111, 6913, 799933, 739138093, 44841044309, 32285551902481, 9879378882159187, 1251387991740163687, 1734423756551866870183, 136771701945232930334431, 23048564587067030852654113, 42769754577382930342215977687, 409306551305554643375006906464591

Offset: 0

Author

Ilya Gutkovskiy, May 24 2022

Keywords

• nonn
• frac

Examples

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

Crossrefs

Cf. A010050, A053557, A061354, A073743, A103816, A120265, A143382, A354211, A354332, A354335 (denominators).

Programs

Mathematica

Table[Sum[1/(2 k)!, {k, 0, n}], {n, 0, 15}] // Numerator
nmax = 15; CoefficientList[Series[Cosh[Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Numerator
Accumulate[1/(2*Range[0,20])!]//Numerator (* Harvey P. Dale, Sep 05 2024 *)

PARI

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

Python

from fractions import Fraction
from math import factorial
def A354334(n): return sum(Fraction(1,factorial(2*k)) for k in range(n+1)).numerator # Chai Wah Wu, May 24 2022

Formula

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