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A336610 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(-sqrt(x) * BesselI(1,2*sqrt(x))). 0
1, -1, 0, 9, -4, -625, -906, 145187, 1350040, -71822385, -2093778910, 49843036199, 4422338360340, 7491520000835, -11939082153832302, -455740256735697165, 33146485198521406064, 4039886119274766333343, 2019781328116371668154 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..18.

FORMULA

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

MATHEMATICA

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}]

CROSSREFS

Cf. A003725, A292952, A302397, A336209, A336227.

Sequence in context: A038294 A214102 A321575 * A293100 A195360 A177973

Adjacent sequences:  A336607 A336608 A336609 * A336611 A336612 A336613

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jul 28 2020

STATUS

approved

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Last modified May 26 13:17 EDT 2022. Contains 354092 sequences. (Running on oeis4.)