A355994 Expansion of e.g.f. -LambertW(x^2/2 * log(1-x)).
0, 0, 0, 3, 6, 20, 270, 1764, 12600, 169560, 1937880, 22300740, 349806600, 5556245760, 89073856872, 1678920566400, 33550354656000, 687175528253760, 15462823882213440, 370285712520237360, 9180722384533375200, 242398467521271149760
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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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 *) -
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)!));
Formula
a(n) = n! * Sum_{k=1..floor(n/3)} k^(k-1) * |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).