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 A354332 #13 May 24 2022 12:55:01
%S A354332 1,5,101,4241,305353,33588829,209594293,1100370038249,23023126954133,
%T A354332 102360822438075317,42991545423991633141,4350744396907953273869,
%U A354332 13052233190723859821607001,9162667699888149594768114701,7440086172309177470951709137213,364172638960396581472899447242531
%N A354332 a(n) is the numerator of Sum_{k=0..n} (-1)^k / (2*k+1)!.
%F A354332 Numerators of coefficients in expansion of sin(sqrt(x)) / (sqrt(x) * (1 - x)).
%e A354332 1, 5/6, 101/120, 4241/5040, 305353/362880, 33588829/39916800, 209594293/249080832, ...
%t A354332 Table[Sum[(-1)^k/(2 k + 1)!, {k, 0, n}], {n, 0, 15}] // Numerator
%t A354332 nmax = 15; CoefficientList[Series[Sin[Sqrt[x]]/(Sqrt[x] (1 - x)), {x, 0, nmax}], x] // Numerator
%o A354332 (PARI) a(n) = numerator(sum(k=0, n, (-1)^k/(2*k+1)!)); \\ _Michel Marcus_, May 24 2022
%o A354332 (Python)
%o A354332 from fractions import Fraction
%o A354332 from math import factorial
%o A354332 def A354332(n): return sum(Fraction(-1 if k % 2 else 1,factorial(2*k+1)) for k in range(n+1)).numerator # _Chai Wah Wu_, May 24 2022
%Y A354332 Cf. A009445, A049469, A053557, A061354, A103816, A120265, A143382, A354211, A354298, A354333 (denominators), A354334.
%K A354332 nonn,frac
%O A354332 0,2
%A A354332 _Ilya Gutkovskiy_, May 24 2022