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Revision History for A277474

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A277474

E.g.f.: -exp(-x)*LambertW(-x).
(history; published version)

#10 by Bruno Berselli at Wed Nov 08 02:29:33 EST 2017

STATUS

reviewed

approved

#9 by Michel Marcus at Wed Nov 08 00:59:58 EST 2017

STATUS

proposed

reviewed

#8 by G. C. Greubel at Tue Nov 07 22:39:31 EST 2017

STATUS

editing

proposed

#7 by G. C. Greubel at Tue Nov 07 22:39:22 EST 2017

LINKS

G. C. Greubel, <a href="/A277474/b277474.txt">Table of n, a(n) for n = 0..385</a>

PROG

(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-exp(-x)*lambertw(-x)))) \\ G. C. Greubel, Nov 07 2017

STATUS

approved

editing

#6 by Vaclav Kotesovec at Mon Oct 17 03:35:14 EDT 2016

STATUS

editing

approved

#5 by Vaclav Kotesovec at Mon Oct 17 03:27:52 EDT 2016

FORMULA

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

#4 by Vaclav Kotesovec at Mon Oct 17 03:26:20 EDT 2016

MATHEMATICA

Table[Sum[(-1)^(n-k)*Binomial[n, k]*k^(k-1), {k, 1, n}], {n, 0, 20}]

#3 by Vaclav Kotesovec at Mon Oct 17 03:24:05 EDT 2016

CROSSREFS

Cf. A000169, A069856, A086331, A277473.

#2 by Vaclav Kotesovec at Mon Oct 17 03:19:16 EDT 2016

NAME

allocated for Vaclav Kotesovec

E.g.f.: -exp(-x)*LambertW(-x).

DATA

0, 1, 0, 6, 36, 380, 4830, 74382, 1342712, 27825912, 651274650, 16994464850, 489240628932, 15404364096420, 526634857318934, 19428038813967630, 769280055136105200, 32543192449030871792, 1464827827285673677746, 69903432558329996409642, 3525344776953738276010940

OFFSET

0,4

FORMULA

a(n) ~ exp(-exp(-1)) * n^(n-1).

MATHEMATICA

CoefficientList[Series[-Exp[-x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!

CROSSREFS

Cf. A069856, A086331, A277473.

KEYWORD

allocated

nonn

AUTHOR

Vaclav Kotesovec, Oct 17 2016

STATUS

approved

editing

#1 by Vaclav Kotesovec at Mon Oct 17 03:16:20 EDT 2016

NAME

allocated for Vaclav Kotesovec

KEYWORD

allocated

STATUS

approved