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A336610
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Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(-sqrt(x) * BesselI(1,2*sqrt(x))).
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0
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1, -1, 0, 9, -4, -625, -906, 145187, 1350040, -71822385, -2093778910, 49843036199, 4422338360340, 7491520000835, -11939082153832302, -455740256735697165, 33146485198521406064, 4039886119274766333343, 2019781328116371668154
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..18.
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FORMULA
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a(0) = 1; a(n) = -n * Sum_{k=0..n-1} binomial(n-1,k)^2 * a(k).
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MATHEMATICA
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nmax = 18; CoefficientList[Series[Exp[-Sqrt[x] BesselI[1, 2 Sqrt[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2
a[0] = 1; a[n_] := a[n] = -n Sum[Binomial[n - 1, k]^2 a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
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CROSSREFS
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Cf. A003725, A292952, A302397, A336209, A336227.
Sequence in context: A038294 A214102 A321575 * A293100 A195360 A177973
Adjacent sequences: A336607 A336608 A336609 * A336611 A336612 A336613
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KEYWORD
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sign
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AUTHOR
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Ilya Gutkovskiy, Jul 28 2020
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STATUS
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approved
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