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 A354331 #12 May 24 2022 12:54:56
%S A354331 1,6,40,5040,362880,13305600,6227020800,1307674368000,513257472000,
%T A354331 121645100408832000,51090942171709440000,8617338912961658880000,
%U A354331 15511210043330985984000000,10888869450418352160768000000,2947253997913233984847872000000,1174691236311131831103651840000000
%N A354331 a(n) is the denominator of Sum_{k=0..n} 1 / (2*k+1)!.
%F A354331 Denominators of coefficients in expansion of sinh(sqrt(x)) / (sqrt(x) * (1 - x)).
%e A354331 1, 7/6, 47/40, 5923/5040, 426457/362880, 15636757/13305600, 7318002277/6227020800, ...
%t A354331 Table[Sum[1/(2 k + 1)!, {k, 0, n}], {n, 0, 15}] // Denominator
%t A354331 nmax = 15; CoefficientList[Series[Sinh[Sqrt[x]]/(Sqrt[x] (1 - x)), {x, 0, nmax}], x] // Denominator
%o A354331 (PARI) a(n) = denominator(sum(k=0, n, 1/(2*k+1)!)); \\ _Michel Marcus_, May 24 2022
%o A354331 (Python)
%o A354331 from fractions import Fraction
%o A354331 from math import factorial
%o A354331 def A354331(n): return sum(Fraction(1,factorial(2*k+1)) for k in range(n+1)).denominator # _Chai Wah Wu_, May 24 2022
%Y A354331 Cf. A009445, A053556, A061355, A073742, A143383, A289488, A354211 (numerators), A354333, A354335.
%K A354331 nonn,frac
%O A354331 0,2
%A A354331 _Ilya Gutkovskiy_, May 24 2022