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 A354333 #12 May 24 2022 12:55:04
%S A354333 1,6,120,5040,362880,39916800,249080832,1307674368000,27360571392000,
%T A354333 121645100408832000,51090942171709440000,5170403347776995328000,
%U A354333 15511210043330985984000000,10888869450418352160768000000,8841761993739701954543616000000,432780981798838043038187520000000
%N A354333 a(n) is the denominator of Sum_{k=0..n} (-1)^k / (2*k+1)!.
%F A354333 Denominators of coefficients in expansion of sin(sqrt(x)) / (sqrt(x) * (1 - x)).
%e A354333 1, 5/6, 101/120, 4241/5040, 305353/362880, 33588829/39916800, 209594293/249080832, ...
%t A354333 Table[Sum[(-1)^k/(2 k + 1)!, {k, 0, n}], {n, 0, 15}] // Denominator
%t A354333 nmax = 15; CoefficientList[Series[Sin[Sqrt[x]]/(Sqrt[x] (1 - x)), {x, 0, nmax}], x] // Denominator
%o A354333 (PARI) a(n) = denominator(sum(k=0, n, (-1)^k/(2*k+1)!)); \\ _Michel Marcus_, May 24 2022
%o A354333 (Python)
%o A354333 from fractions import Fraction
%o A354333 from math import factorial
%o A354333 def A354333(n): return sum(Fraction(-1 if k % 2 else 1,factorial(2*k+1)) for k in range(n+1)).denominator # _Chai Wah Wu_, May 24 2022
%Y A354333 Cf. A009445, A049469, A053556, A061355, A143383, A354299, A354331, A354332 (numerators), A354335.
%K A354333 nonn,frac
%O A354333 0,2
%A A354333 _Ilya Gutkovskiy_, May 24 2022