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A355993
Expansion of e.g.f. -LambertW(x^3 * log(1-x))/6.
1
0, 0, 0, 0, 4, 10, 40, 210, 8064, 70560, 640800, 6375600, 189383040, 3165402240, 48879754560, 762766804800, 21652937349120, 525738717504000, 11796584629939200, 259139188966694400, 7842638783736115200, 240231375437935795200, 7066934411387842252800
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