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A335946
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a(n) = 1 + Sum_{k=0..n-1} binomial(n,k)^2 * a(k).
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1
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1, 2, 10, 110, 2154, 65902, 2903446, 174109546, 13636888810, 1351801926542, 165434393561910, 24497621303302666, 4317170011370444982, 892891315599103615082, 214174328063904077240962, 58974283594413521123672110, 18476316023495768160707616490
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OFFSET
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0,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..248
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FORMULA
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Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselI(0,2*sqrt(x)) / (2 - BesselI(0,2*sqrt(x))).
a(n) = 2 * A102221(n) for n > 0.
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MATHEMATICA
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a[n_] := a[n] = 1 + Sum[Binomial[n, k]^2 a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(2 - BesselI[0, 2 Sqrt[x]]), {x, 0, nmax}], x] Range[0, nmax]!^2
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CROSSREFS
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Row sums of A102220.
Cf. A000629, A102221.
Sequence in context: A006608 A066205 A113147 * A206154 A181445 A231969
Adjacent sequences: A335943 A335944 A335945 * A335947 A335948 A335949
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Jul 01 2020
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STATUS
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approved
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