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%I #6 May 24 2022 02:39:24
%S 1,0,1,2,43,403,23213,118483,51997111,1842647621,327581799289,
%T 8918414485643,4670006130663971,361730891537680087,
%U 130890931830249779173,427294615628884602769,6534075316966068976316143,885163015595247156635327497,41526561745210509140249210357
%N a(n) is the numerator of Sum_{k=0..n} (-1)^k / (k!)^2.
%F Numerators of coefficients in expansion of BesselJ(0,2*sqrt(x)) / (1 - x).
%e 1, 0, 1/4, 2/9, 43/192, 403/1800, 23213/103680, 118483/529200, 51997111/232243200, 1842647621/8230118400, ...
%t Table[Sum[(-1)^k/(k!)^2, {k, 0, n}], {n, 0, 18}] // Numerator
%t nmax = 18; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Numerator
%Y Cf. A001044, A053557, A061354, A073701, A091681, A103816, A120265, A143382, A354302, A354305 (denominators).
%K nonn,frac
%O 0,4
%A _Ilya Gutkovskiy_, May 23 2022
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