A357321 Expansion of e.g.f. -LambertW(log(1 - 2*x)/2).

0, 1, 4, 29, 308, 4349, 77094, 1650893, 41532280, 1201865049, 39351776970, 1438731784137, 58107225611412, 2569486856423733, 123475320944016846, 6407225728624769925, 357061085760608504304, 21268522319028809507889, 1348496822257863921774738

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Lambert W-Function.

Index entries for reversions of series

Formula

a(n) = Sum_{k=1..n} 2^(n-k) * k^(k-1) * |Stirling1(n,k)|.

a(n) ~ 2^(n - 1/2) * n^(n-1) / ((-1 + exp(2*exp(-1)))^(n - 1/2) * exp(n - 2*n*exp(-1) - 1/2)). - Vaclav Kotesovec, Oct 04 2022

E.g.f.: Series_Reversion( (1 - exp(-2 * x * exp(-x)))/2 ). - Seiichi Manyama, Sep 11 2024

Mathematica

With[{m = 20}, Range[0, m]! * CoefficientList[Series[-ProductLog[Log[1 - 2*x]/2], {x, 0, m}], x]] (* Amiram Eldar, Sep 24 2022 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(log(1-2*x)/2))))
(PARI) a(n) = sum(k=1, n, 2^(n-k)*k^(k-1)*abs(stirling(n, k, 1)));

Crossrefs

Cf. A052807, A357322.

Cf. A357333.

Sequence in context: A360834 A349599 A214654 * A067146 A210949 A014622

Adjacent sequences: A357318 A357319 A357320 * A357322 A357323 A357324

Keyword

nonn

Author

Seiichi Manyama, Sep 24 2022

Status

approved