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A277457 E.g.f.: exp(2*x)/(1+LambertW(-x)). 3
1, 3, 12, 71, 616, 7197, 105052, 1829291, 36922928, 846851993, 21744781684, 617832652527, 19242299657896, 651815827343189, 23857403245171724, 938247816632341043, 39455261828928309088, 1766645684585351990961, 83913998998426051745764, 4214295288128637488870327, 223120214856875472660345176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) ~ exp(2*exp(-1)) * n^n.

MATHEMATICA

CoefficientList[Series[Exp[2*x]/(1+LambertW[-x]), {x, 0, 20}], x]*Range[0, 20]!

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

Table[2^n + Sum[Binomial[n, k]*2^(n-k)*k^k, {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2016 *)

PROG

(PARI) x='x+O('x^50); Vec(serlaplace(exp(2*x)/(1 + lambertw(-x)))) \\ G. C. Greubel, Nov 07 2017

CROSSREFS

Cf. A086331, A277454, A277456, A277485.

Sequence in context: A330493 A112320 A103366 * A228386 A175836 A293138

Adjacent sequences:  A277454 A277455 A277456 * A277458 A277459 A277460

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 16 2016

STATUS

approved

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Last modified April 5 15:53 EDT 2020. Contains 333245 sequences. (Running on oeis4.)