# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a136461 Showing 1-1 of 1 %I A136461 #34 Oct 27 2023 21:01:02 %S A136461 1,1,3,14,96,849,9362,123101,1888016,33066768,651883152,14286514186, %T A136461 344690210928,9079702374300,259327537407416,7983107543564724, %U A136461 263518937698466304,9285770278110061664,347916420499685643072,13812127364516107258944,579183295530010157485824 %N A136461 Expansion of e.g.f.: A(x) = -(1 + LambertW(-log(1+x))/log(1+x))/x. %C A136461 A033917 gives the coefficients of iterated exponential function defined by y(x) = x^y(x) expanded about x=1. %H A136461 Alois P. Heinz, Table of n, a(n) for n = 0..400 (first 71 terms from Vincenzo Librandi) %F A136461 a(n) = A033917(n+1)/(n+1). %F A136461 E.g.f.: A(x) = (1/x)*Sum_{i>=1} (i+1)^(i-1) * log(1+x)^i/i!. %F A136461 a(n) ~ n^(n-1) / ( exp(n-3/2+exp(-1)/2) * (exp(exp(-1))-1)^(n+1/2) ). - _Vaclav Kotesovec_, Nov 27 2012 %p A136461 a:= n-> add(Stirling1(n+1, k)*(k+1)^(k-1), k=0..n+1)/(n+1): %p A136461 seq(a(n), n=0..25); # _Alois P. Heinz_, Jan 21 2016 %t A136461 CoefficientList[Series[-(1+LambertW[-Log[1+x]]/Log[1+x])/x, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Nov 27 2012 *) %o A136461 (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)} %o A136461 (PARI) x='x+O('x^30); Vec(serlaplace(-(1+lambertw(-log(1+x))/log(1+x))/x )) \\ _G. C. Greubel_, Feb 19 2018 %Y A136461 Cf. A033917. %Y A136461 Row sums of A295027 (shifted). %Y A136461 Main diagonal of A295028 (shifted). %K A136461 nonn %O A136461 0,3 %A A136461 _Paul D. Hanna_, Dec 31 2007 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE