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A336209 a(0) = 1; a(n) = -(1/n) * Sum_{k=0..n-1} binomial(n,k)^2 * (n-k) * a(k). 4
1, -1, 1, 2, -15, -46, 880, 5837, -132783, -2109238, 35966256, 1440196097, -8909037720, -1504006716551, -16097564749643, 2021100230840147, 83130656159529937, -2475528081920694566, -331363460045748820376, -3874344448291316066455, 1255007424437046915956520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) = (n!)^2 * [x^n] exp(-Sum_{k>=1} x^k / (k!)^2).

a(n) = (n!)^2 * [x^n] exp(1 - BesselI(0,2*sqrt(x))).

MATHEMATICA

a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Binomial[n, k]^2 (n - k) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 20}]

nmax = 20; CoefficientList[Series[Exp[-Sum[x^k/(k!)^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^2

CROSSREFS

Cf. A000587, A023998, A336210.

Sequence in context: A162256 A229013 A323685 * A256328 A041719 A133777

Adjacent sequences:  A336206 A336207 A336208 * A336210 A336211 A336212

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jul 12 2020

STATUS

approved

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Last modified August 3 01:55 EDT 2021. Contains 346429 sequences. (Running on oeis4.)