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%I #5 Jan 25 2021 19:04:48
%S 1,1,6,76,1720,60816,3096384,214579296,19422473088,2224980891904,
%T 314675568756736,53849929134122496,10966912240761425920,
%U 2621246193301011159040,726608751113679704248320,231217063994112487051984896,83713709650818121936828858368
%N a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * 2^(n-k-1) * a(k).
%F Sum_{n>=0} a(n) * x^n / (n!)^2 = 2 / (3 - BesselI(0,2*sqrt(2*x))).
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^2 2^(n - k - 1) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
%t nmax = 16; CoefficientList[Series[2/(3 - BesselI[0, 2 Sqrt[2 x]]), {x, 0, nmax}], x] Range[0, nmax]!^2
%Y Cf. A102221, A122704, A340887, A340888.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jan 25 2021