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%I
%S 1,2,10,110,2154,65902,2903446,174109546,13636888810,1351801926542,
%T 165434393561910,24497621303302666,4317170011370444982,
%U 892891315599103615082,214174328063904077240962,58974283594413521123672110,18476316023495768160707616490
%N a(n) = 1 + Sum_{k=0..n-1} binomial(n,k)^2 * a(k).
%H Seiichi Manyama, <a href="/A335946/b335946.txt">Table of n, a(n) for n = 0..248</a>
%F Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselI(0,2*sqrt(x)) / (2 - BesselI(0,2*sqrt(x))).
%F a(n) = 2 * A102221(n) for n > 0.
%t a[n_] := a[n] = 1 + Sum[Binomial[n, k]^2 a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
%t nmax = 16; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(2 - BesselI[0, 2 Sqrt[x]]), {x, 0, nmax}], x] Range[0, nmax]!^2
%Y Row sums of A102220.
%Y Cf. A000629, A102221.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Jul 01 2020
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