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 A354298 #18 Jan 10 2024 23:55:37
%S A354298 1,2,11,76,137,7534,97943,1469144,24975449,94906706,9965204131,
%T A354298 229199695012,5729992375301,9100576125478,897316805972131,
%U A354298 563093542209232,4589775462547450033,5539384178936577626,5943759223998947792699,46361321947191792783052,9504070999174317520525661
%N A354298 a(n) is the numerator of Sum_{k=1..n} (-1)^(k+1) / (2*k-1)!!.
%H A354298 Robert Israel, <a href="/A354298/b354298.txt">Table of n, a(n) for n = 1..403</a>
%F A354298 Numerators of coefficients in expansion of sqrt(Pi*x*exp(-x)/2) * erfi(sqrt(x/2)) / (1 - x).
%e A354298 1, 2/3, 11/15, 76/105, 137/189, 7534/10395, 97943/135135, 1469144/2027025, 24975449/34459425, ...
%p A354298 S:= 0: R:= NULL:
%p A354298 for n from 1 to 100 do
%p A354298 S:= S + (-1)^(n+1)/doublefactorial(2*n-1);
%p A354298 R:= R, numer(S);
%p A354298 od:
%p A354298 R; # _Robert Israel_, Jan 10 2024
%t A354298 Table[Sum[(-1)^(k + 1)/(2 k - 1)!!, {k, 1, n}], {n, 1, 21}] // Numerator
%t A354298 nmax = 21; CoefficientList[Series[Sqrt[Pi x Exp[-x]/2] Erfi[Sqrt[x/2]]/(1 - x), {x, 0, nmax}], x] // Numerator // Rest
%t A354298 Table[1/(1 + ContinuedFractionK[2 k - 1, 2 k, {k, 1, n - 1}]), {n, 1, 21}] // Numerator
%Y A354298 Cf. A001147, A053557, A061354, A064646, A103816, A113012, A120265, A143382, A289381, A306858, A354299 (denominators).
%K A354298 nonn,frac
%O A354298 1,2
%A A354298 _Ilya Gutkovskiy_, May 23 2022