login
A355994
Expansion of e.g.f. -LambertW(x^2/2 * log(1-x)).
1
0, 0, 0, 3, 6, 20, 270, 1764, 12600, 169560, 1937880, 22300740, 349806600, 5556245760, 89073856872, 1678920566400, 33550354656000, 687175528253760, 15462823882213440, 370285712520237360, 9180722384533375200, 242398467521271149760
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * Sum_{k=1..floor(n/3)} k^(k-1) * |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).
MATHEMATICA
With[{m = 25}, Range[0, m]! * CoefficientList[Series[-ProductLog[x^2/2 * Log[1 - x]], {x, 0, m}], x]] (* Amiram Eldar, Sep 24 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); concat([0, 0, 0], Vec(serlaplace(-lambertw(x^2/2*log(1-x)))))
(PARI) a(n) = n!*sum(k=1, n\3, k^(k-1)*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 24 2022
STATUS
approved