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%I #8 Sep 04 2020 10:07:07
%S 0,1,7,82,1839,69630,3950650,313747050,33224570175,4523562983350,
%T 769859662962750,160137417877796250,39971947204607486250,
%U 11791483690935887486250,4058152793413483423916250,1611522009185095020022068750,731368135285580087866788609375,376178084508304435598172207843750
%N a(0) = 0; a(n) = 5^(n-1) + (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * 5^(k-1) * (n-k) * a(n-k).
%F Sum_{n>=0} a(n) * x^n / (n!)^2 = -log((6 - BesselI(0,2*sqrt(5*x))) / 5).
%t a[0] = 0; a[n_] := a[n] = 5^(n - 1) + (1/n) Sum[Binomial[n, k]^2 5^(k - 1) (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n],{n, 0, 17}]
%t nmax = 17; CoefficientList[Series[-Log[(6 - BesselI[0, 2 Sqrt[5 x]])/5], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y Cf. A102223, A333981, A333982, A333983, A333985, A337595.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 04 2020
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