A277465 -id:A277465 - cp's OEIS frontend

A277466 E.g.f.: -log(1-x)/(1+LambertW(-x)).

0, 1, 3, 17, 146, 1684, 24294, 419383, 8412760, 192078864, 4914973770, 139265564723, 4327699948956, 146323675764044, 5347193667136398, 210005149832116455, 8820722263274822992, 394546588041904397184, 18723398414958791004690, 939550079246853331267203

Offset: 0

Vaclav Kotesovec, Oct 16 2016

nonn

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

Cf. A000312, A086331, A277465.

CoefficientList[Series[-Log[1-x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Flatten[{0, Table[(n-1)! + n!*Sum[k^k/(k!*(n-k)), {k, 1, n-1}], {n, 1, 25}]}] (* Vaclav Kotesovec, Oct 28 2016 *)

x='x+O('x^50); concat([0], Vec(serlaplace(-log(1-x)/(1 + lambertw(-x))))) \\ G. C. Greubel, Nov 07 2017

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

A277481 E.g.f.: -log(1+x)*LambertW(-x).

Original entry on oeis.org

0, 0, 2, 3, 32, 240, 3114, 44065, 777720, 15582168, 357427770, 9151281293, 259607392164, 8070381333872, 272960010908662, 9976300661919345, 391837137436921072, 16458193396472517328, 736145006794621566642, 34932117830021859779517, 1752782822664497750549660

Offset: 0

Vaclav Kotesovec, Oct 17 2016

nonn

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

Cf. A000169, A277465, A277473, A277482.

CoefficientList[Series[-Log[1+x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[n!*Sum[(-1)^(n-k-1)*k^(k-1)/(k!*(n-k)), {k, 1, n-1}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2016 *)

x='x+O('x^50); concat([0,0], Vec(serlaplace(-log(1+x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 08 2017

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

cp's OEIS Frontend

A277466 E.g.f.: -log(1-x)/(1+LambertW(-x)).

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