OFFSET
1,2
FORMULA
E.g.f.: -LambertW(-x) / (1 - LambertW(-x)^2).
a(n) = n * A133297(n).
MATHEMATICA
Table[n! Sum[(-1)^(k + 1) n^(n - k)/(n - k)!, {k, 1, n}], {n, 1, 20}]
nmax = 20; CoefficientList[Series[-LambertW[-x]/(1 - LambertW[-x]^2), {x, 0, nmax}], x] Range[0, nmax]! // Rest
PROG
(PARI) a(n) = n! * sum(k=1, n, (-1)^(k+1)*n^(n-k)/(n-k)!); \\ Michel Marcus, Sep 23 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 23 2021
STATUS
approved