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 A335946 a(n) = 1 + Sum_{k=0..n-1} binomial(n,k)^2 * a(k). 1

%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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Last modified March 29 01:21 EDT 2023. Contains 361596 sequences. (Running on oeis4.)