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%I #5 Jul 15 2021 21:21:26
%S 0,1,-3,4,-8,1,353,27224,1871840,147012849,13684928021,1514370713340,
%T 197964773810648,30300949591876913,5380510834911767033,
%U 1098630080602791984784,255851291397441057781120,67450889282916741495608737,19994198644782014829579657837,6623096362909598587714211804212
%N a(n) = (n!)^2 * Sum_{k=0..n-1} (-1)^k / ((n-k) * k!)^2.
%F Sum_{n>=0} a(n) * x^n / (n!)^2 = polylog(2,x) * BesselJ(0,2*sqrt(x)).
%t Table[(n!)^2 Sum[(-1)^k/((n - k) k!)^2, {k, 0, n - 1}], {n, 0, 19}]
%t nmax = 19; CoefficientList[Series[PolyLog[2, x] BesselJ[0, 2 Sqrt[x]], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y Cf. A002741, A073701, A336292, A340789, A346410.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Jul 15 2021
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