OFFSET
0,3
COMMENTS
A033917 gives the coefficients of iterated exponential function defined by y(x) = x^y(x) expanded about x=1.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..400 (first 71 terms from Vincenzo Librandi)
FORMULA
a(n) = A033917(n+1)/(n+1).
E.g.f.: A(x) = (1/x)*Sum_{i>=1} (i+1)^(i-1) * log(1+x)^i/i!.
a(n) ~ n^(n-1) / ( exp(n-3/2+exp(-1)/2) * (exp(exp(-1))-1)^(n+1/2) ). - Vaclav Kotesovec, Nov 27 2012
MAPLE
a:= n-> add(Stirling1(n+1, k)*(k+1)^(k-1), k=0..n+1)/(n+1):
seq(a(n), n=0..25); # Alois P. Heinz, Jan 21 2016
MATHEMATICA
CoefficientList[Series[-(1+LambertW[-Log[1+x]]/Log[1+x])/x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 27 2012 *)
PROG
(PARI) {a(n)=n!*polcoeff(sum(i=0, n+1, (i+1)^(i-1)*log(1+x +O(x^(n+2) ))^i/i!), n+1)}
(PARI) x='x+O('x^30); Vec(serlaplace(-(1+lambertw(-log(1+x))/log(1+x))/x )) \\ G. C. Greubel, Feb 19 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 31 2007
STATUS
approved