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 A354299 #10 Jan 10 2024 23:55:50
%S A354299 1,3,15,105,189,10395,135135,2027025,34459425,130945815,13749310575,
%T A354299 316234143225,7905853580625,12556355686875,1238056670725875,
%U A354299 776918153694375,6332659870762850625,7642865361265509375,8200794532637891559375,63966197354575554163125,13113070457687988603440625
%N A354299 a(n) is the denominator of Sum_{k=1..n} (-1)^(k+1) / (2*k-1)!!.
%H A354299 Robert Israel, <a href="/A354299/b354299.txt">Table of n, a(n) for n = 1..403</a>
%F A354299 Denominators of coefficients in expansion of sqrt(Pi*x*exp(-x)/2) * erfi(sqrt(x/2)) / (1 - x).
%e A354299 1, 2/3, 11/15, 76/105, 137/189, 7534/10395, 97943/135135, 1469144/2027025, 24975449/34459425, ...
%p A354299 S:= 0: R:= NULL:
%p A354299 for n from 1 to 100 do
%p A354299 S:= S + (-1)^(n+1)/doublefactorial(2*n-1);
%p A354299 R:= R, denom(S);
%p A354299 od:
%p A354299 R; # _Robert Israel_, Jan 10 2024
%t A354299 Table[Sum[(-1)^(k + 1)/(2 k - 1)!!, {k, 1, n}], {n, 1, 21}] // Denominator
%t A354299 nmax = 21; CoefficientList[Series[Sqrt[Pi x Exp[-x]/2] Erfi[Sqrt[x/2]]/(1 - x), {x, 0, nmax}], x] // Denominator // Rest
%t A354299 Table[1/(1 + ContinuedFractionK[2 k - 1, 2 k, {k, 1, n - 1}]), {n, 1, 21}] // Denominator
%Y A354299 Cf. A001147, A053556, A061355, A064647, A113013, A143383, A289488, A306858, A354298 (numerators).
%K A354299 nonn,frac
%O A354299 1,2
%A A354299 _Ilya Gutkovskiy_, May 23 2022