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A334316 E.g.f. A(x) satisfies: A(x) = x * exp(A(x)) * (1 - A(x)). 1
1, 0, -3, -8, 45, 576, 385, -54144, -499527, 4787200, 160740261, 558627840, -45943496027, -854266871808, 8403892043625, 590895130771456, 4982009666876145, -320936968832679936, -10133752613818727987, 75595253378088960000, 11587542472638176520861 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Exponential reversion of A000240 (rencontres numbers).

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..400

Index entries for reversions of series

FORMULA

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

MATHEMATICA

nmax = 21; CoefficientList[InverseSeries[Series[x Exp[-x]/(1 - x), {x, 0, nmax}], x], x] Range[0, nmax]! // Rest

Table[(n - 1)! Sum[(-1)^k Binomial[n, k] n^(n - k - 1)/(n - k - 1)!, {k, 0, n - 1}], {n, 1, 21}]

Table[HypergeometricU[1 - n, 2, n], {n, 1, 21}]

CROSSREFS

Cf. A000240, A052885.

Sequence in context: A000240 A182390 A132103 * A180508 A040018 A019016

Adjacent sequences:  A334313 A334314 A334315 * A334317 A334318 A334319

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Apr 22 2020

STATUS

approved

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Last modified May 30 08:43 EDT 2020. Contains 334712 sequences. (Running on oeis4.)