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 A136461 Expansion of e.g.f.: A(x) = -(1 + LambertW(-log(1+x))/log(1+x))/x. 3
 1, 1, 3, 14, 96, 849, 9362, 123101, 1888016, 33066768, 651883152, 14286514186, 344690210928, 9079702374300, 259327537407416, 7983107543564724, 263518937698466304, 9285770278110061664, 347916420499685643072, 13812127364516107258944, 579183295530010157485824 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A033917 gives the coefficients of iterated exponential function defined by y(x) = x^y(x) expanded about x=1. LINKS Vincenzo Librandi and 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 Cf. A033917. Row sums of A295027 (shifted). Main diagonal of A295028 (shifted). Sequence in context: A295108 A295109 A295110 * A336525 A345106 A276747 Adjacent sequences:  A136458 A136459 A136460 * A136462 A136463 A136464 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 31 2007 STATUS approved

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Last modified August 2 07:36 EDT 2021. Contains 346411 sequences. (Running on oeis4.)