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A357267
Expansion of e.g.f. -LambertW(x * (1 - exp(x))).
5
0, 0, 2, 3, 28, 125, 1506, 12607, 186600, 2352681, 41839750, 705821171, 14818593516, 311784460429, 7603945309338, 190868446707135, 5328147004384336, 154893585657590609, 4884408906341245326, 161057122218190660555, 5671407469802947722900
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * Sum_{k=1..floor(n/2)} k^(k-1) * Stirling2(n-k,k)/(n-k)!.
PROG
(PARI) my(N=20, x='x+O('x^N)); concat([0, 0], Vec(serlaplace(-lambertw(x*(1-exp(x))))))
(PARI) a(n) = n!*sum(k=1, n\2, k^(k-1)*stirling(n-k, k, 2)/(n-k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 21 2022
STATUS
approved