A355995 Expansion of e.g.f. -LambertW(x^3/6 * log(1-x)).

0, 0, 0, 0, 4, 10, 40, 210, 2464, 20160, 178800, 1755600, 22323840, 289729440, 3950069760, 57127870800, 921032555520, 15786602832000, 284810759251200, 5394363163862400, 108742028591923200, 2312415679065811200, 51543520889668684800, 1199641884471310156800

Offset

0,5

Links

Table of n, a(n) for n=0..23.

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

Formula

a(n) = n! * Sum_{k=1..floor(n/4)} k^(k-1) * |Stirling1(n-3*k,k)|/(6^k * (n-3*k)!).

Mathematica

With[{m = 25}, Range[0, m]! * CoefficientList[Series[-ProductLog[x^3/6 * Log[1 - x]], {x, 0, m}], x]] (* Amiram Eldar, Sep 24 2022 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(serlaplace(-lambertw(x^3/6*log(1-x)))))
(PARI) a(n) = n!*sum(k=1, n\4, k^(k-1)*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));

Crossrefs

Cf. A052807, A355994, A357265.

Sequence in context: A351493 A368166 A351506 * A356753 A356968 A375699

Adjacent sequences: A355992 A355993 A355994 * A355996 A355997 A355998

Keyword

nonn

Author

Seiichi Manyama, Sep 24 2022

Status

approved