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A336228 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * (n-k) * a(k). 1

%I

%S 1,1,6,75,1684,59005,2977566,204512875,18346977608,2083115635065,

%T 291996210173410,49525220811387871,9996609976117991436,

%U 2368117724291275331869,650613686811158069472942,205196311013650099853516115,73633144885479474283911225616

%N a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * (n-k) * a(k).

%F a(n) = (n!)^2 * [x^n] 1 / (1 - sqrt(x) * BesselI(1,2*sqrt(x))).

%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^2 (n - k) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]

%t nmax = 16; CoefficientList[Series[1/(1 - Sqrt[x] BesselI[1, 2 Sqrt[x]]), {x, 0, nmax}], x] Range[0, nmax]!^2

%Y Cf. A006153, A102221.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jul 12 2020

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Last modified January 18 17:05 EST 2022. Contains 350455 sequences. (Running on oeis4.)