OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..375
FORMULA
E.g.f.: A(x) = log(1+x)/LambertW(log(1+x)).
log(A(x)) = LambertW(log(1+x)).
E.g.f.: A(x) = 1/G(-x) where G(x) = g.f. of A052813.
E.g.f. of A052807 = -log(A(-x)) = -log(1-x)/A(-x).
a(n) = Sum_{k=0..n} (-1)^(k+1)*Stirling1(n,k)*(k-1)^(k-1). - Vladeta Jovovic, Jul 22 2006
|a(n)| ~ exp((exp(-1)-1)*n+3/2) * n^(n-1) / (exp(exp(-1))-1)^(n-1/2). - Vaclav Kotesovec, Jul 09 2013
MATHEMATICA
CoefficientList[Series[Log[1+x]/LambertW[Log[1+x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jul 09 2013 *)
Table[StirlingS1[n, 0] + StirlingS1[n, 1] + Sum[(-1)^(k + 1)*StirlingS1[n, k]*(k - 1)^(k - 1), {k, 2, n}], {n, 0, 50}] (* G. C. Greubel, Jun 21 2017 *)
CoefficientList[Series[Exp[LambertW[Log[1+x]]], {x, 0, 25}], x]* Range[0, 25]! (* G. C. Greubel, Jun 22 2017 *)
PROG
(PARI) {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[ #A]=-Vec(Ser(A)^Ser(A))[ #A]); n!*A[n+1]}
(PARI) x='x+O('x^50); Vec(serlaplace(exp(lambertw(log(1+x))))) \\ G. C. Greubel, Jun 22 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jul 20 2006
STATUS
approved