A277505 E.g.f.: -LambertW(-x)/(1-x).

0, 1, 4, 21, 148, 1365, 15966, 229411, 3932440, 78438681, 1784386810, 45565679511, 1289796524820, 40065439945141, 1354630932486118, 49512390012682395, 1945119744809765296, 81728227537432878513, 3657019655412488345202, 173610723750748520091679

Offset

0,3

Links

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

Formula

For n > 0, a(n) = Sum_{k=1..n} 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[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, A277511.

Sequence in context: A247054 A006153 A286286 * A183387 A346430 A324236

Adjacent sequences: A277502 A277503 A277504 * A277506 A277507 A277508

Keyword

nonn

Author

Vaclav Kotesovec, Oct 18 2016

Status

approved