OFFSET
0,5
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = (n!/6) * Sum_{k=1..floor(n/4)} k^(k-1) * |Stirling1(n-3*k,k)|/(n-3*k)!.
MATHEMATICA
With[{m = 25}, Range[0, m]! * CoefficientList[Series[-ProductLog[x^3 * Log[1 - x]]/6, {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*log(1-x)))/6))
(PARI) a(n) = n!*sum(k=1, n\4, k^(k-1)*abs(stirling(n-3*k, k, 1))/(n-3*k)!)/6;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 24 2022
STATUS
approved