%I #5 Jul 15 2021 21:21:20
%S 0,1,5,22,152,2001,45097,1527506,71864928,4466430513,353828600029,
%T 34770661312190,4148422395161464,590479899466175681,
%U 98824492409739430401,19209838771051338898234,4291488438323868507946880,1091819942877526843993466529,313819508664449992611846900981
%N a(n) = (n!)^2 * Sum_{k=0..n-1} 1 / ((n-k) * k!)^2.
%F Sum_{n>=0} a(n) * x^n / (n!)^2 = polylog(2,x) * BesselI(0,2*sqrt(x)).
%t Table[(n!)^2 Sum[1/((n - k) k!)^2, {k, 0, n - 1}], {n, 0, 18}]
%t nmax = 18; CoefficientList[Series[PolyLog[2, x] BesselI[0, 2 Sqrt[x]], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y Cf. A002104, A006040, A066998, A193563, A336291, A346411.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 15 2021
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