A277458 E.g.f.: -1/(1-LambertW(-x)).

-1, 1, 0, 3, 16, 165, 2016, 30415, 539904, 11049129, 256038400, 6627314331, 189517916160, 5933803272397, 201893195083776, 7417376809230375, 292648536838045696, 12341039738944113105, 553942486234823786496, 26369048375194607316019, 1326864458454400696320000

Offset

0,4

Links

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

Jason Saied, Jeffrey Marshall, Namit Anand, and Eleanor G. Rieffel, General protocols for the efficient distillation of indistinguishable photons, arxiv:2404.14217 [quant-ph], Apr 22 2024. See p. 14.

Formula

a(n) ~ n^(n-1) / 4.

a(n) = n!*Sum_{k = 1..n} (-1)^(k+1)*k*n^(n-k-1)/(n-k)! for n >= 1. Cf. A133297. - Peter Bala, Jul 23 2021

Maple

seq(n!*add((-1)^(k+1)*k*n^(n-k-1)/(n-k)!, k = 1..n), n = 1..20); # Peter Bala, Jul 23 2021

Mathematica

CoefficientList[Series[-1/(1-LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!

Prog

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

Crossrefs

Cf. A000312, A086331, A133297, A134095, A277510, A308506.

Sequence in context: A349591 A091146 A350415 * A172402 A297668 A203593

Adjacent sequences: A277455 A277456 A277457 * A277459 A277460 A277461

Keyword

sign,easy

Author

Vaclav Kotesovec, Oct 16 2016

Status

approved