A277457 E.g.f.: exp(2*x)/(1+LambertW(-x)).

1, 3, 12, 71, 616, 7197, 105052, 1829291, 36922928, 846851993, 21744781684, 617832652527, 19242299657896, 651815827343189, 23857403245171724, 938247816632341043, 39455261828928309088, 1766645684585351990961, 83913998998426051745764, 4214295288128637488870327, 223120214856875472660345176

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: A112320 A103366 A335643 * A367117 A228386 A175836

Adjacent sequences: A277454 A277455 A277456 * A277458 A277459 A277460

Keyword

nonn

Author

Vaclav Kotesovec, Oct 16 2016

Status

approved