This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A354334 #15 Sep 05 2024 11:44:55
%S A354334 1,3,37,1111,6913,799933,739138093,44841044309,32285551902481,
%T A354334 9879378882159187,1251387991740163687,1734423756551866870183,
%U A354334 136771701945232930334431,23048564587067030852654113,42769754577382930342215977687,409306551305554643375006906464591
%N A354334 a(n) is the numerator of Sum_{k=0..n} 1 / (2*k)!.
%F A354334 Numerators of coefficients in expansion of cosh(sqrt(x)) / (1 - x).
%e A354334 1, 3/2, 37/24, 1111/720, 6913/4480, 799933/518400, 739138093/479001600, ...
%t A354334 Table[Sum[1/(2 k)!, {k, 0, n}], {n, 0, 15}] // Numerator
%t A354334 nmax = 15; CoefficientList[Series[Cosh[Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Numerator
%t A354334 Accumulate[1/(2*Range[0,20])!]//Numerator (* _Harvey P. Dale_, Sep 05 2024 *)
%o A354334 (PARI) a(n) = numerator(sum(k=0, n, 1/(2*k)!)); \\ _Michel Marcus_, May 24 2022
%o A354334 (Python)
%o A354334 from fractions import Fraction
%o A354334 from math import factorial
%o A354334 def A354334(n): return sum(Fraction(1,factorial(2*k)) for k in range(n+1)).numerator # _Chai Wah Wu_, May 24 2022
%Y A354334 Cf. A010050, A053557, A061354, A073743, A103816, A120265, A143382, A354211, A354332, A354335 (denominators).
%K A354334 nonn,frac
%O A354334 0,2
%A A354334 _Ilya Gutkovskiy_, May 24 2022