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 A354302 #7 May 24 2022 02:38:47
%S A354302 1,2,9,41,1313,5471,1181737,28952557,1235309099,150090055529,
%T A354302 30018011105801,201787741322329,523033825507476769,
%U A354302 44196358255381786981,5774990812036553498851,1949059399062336805862213,997918412319916444601453057,3697415655903280160125896583
%N A354302 a(n) is the numerator of Sum_{k=0..n} 1 / (k!)^2.
%F A354302 Numerators of coefficients in expansion of BesselI(0,2*sqrt(x)) / (1 - x).
%e A354302 1, 2, 9/4, 41/18, 1313/576, 5471/2400, 1181737/518400, 28952557/12700800, 1235309099/541900800, ...
%t A354302 Table[Sum[1/(k!)^2, {k, 0, n}], {n, 0, 17}] // Numerator
%t A354302 nmax = 17; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Numerator
%Y A354302 Cf. A001044, A006040, A053557, A061354, A070910, A103816, A120265, A143382, A354303 (denominators), A354304.
%K A354302 nonn,frac
%O A354302 0,2
%A A354302 _Ilya Gutkovskiy_, May 23 2022