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A277511 E.g.f.: -LambertW(-x)/(1+x). 2
0, 1, 0, 9, 28, 485, 4866, 83587, 1428456, 30190617, 698093830, 18258392471, 523907661036, 16487285529013, 562892775847962, 20749534387671195, 820928954404107856, 34705399650797034929, 1561214366024349903246, 74464277343448593371167, 3753594453131028132576660 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..385

FORMULA

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

a(n) ~ n^(n-1) / (1+exp(-1)).

MATHEMATICA

CoefficientList[Series[-LambertW[-x]/(1+x), {x, 0, 20}], x] * Range[0, 20]!

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

PROG

(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-lambertw(-x)/(1+x)))) \\ G. C. Greubel, Nov 12 2017

CROSSREFS

Cf. A000169, A277505.

Sequence in context: A042501 A271185 A306843 * A041154 A024121 A205144

Adjacent sequences:  A277508 A277509 A277510 * A277512 A277513 A277514

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 18 2016

STATUS

approved

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Last modified August 17 17:08 EDT 2019. Contains 326059 sequences. (Running on oeis4.)