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%I #14 Sep 08 2022 08:45:35
%S 1,7,70,899,14001,255532,5342541,125876003,3300437302,95338188007,
%T 3009043615073,103043811158864,3805827820399125,150819894172935183,
%U 6383815674758486310,287459477551898694403,13721584934214631377921
%N L.g.f.: A(x) = log( Sum_{n>=0} n^n*x^n ) = Sum_{n>=1} a(n)*x^n/n.
%H Seiichi Manyama, <a href="/A141151/b141151.txt">Table of n, a(n) for n = 1..385</a>
%F a(n) ~ n^(n+1). - _Vaclav Kotesovec_, May 30 2019
%e L.g.f.: A(x) = x + 7*x^2/2 + 70*x^3/3 + 899*x^4/4 + 14001*x^5/5 + ...
%e exp(A(x)) = 1 + x + 4*x^2 + 27*x^3 + 256*x^4 + 3125*x^5 + 46656*x^6 + ...
%t With[{m=20}, Drop[CoefficientList[Series[Log[Sum[If[n==0, 1, n^n*x^n], {n, 0, m+2}]], {x, 0, m}], x], 1]*Range[1, m]] (* _G. C. Greubel_, May 30 2019 *)
%o (PARI) {a(n)=polcoeff(x*deriv(log(Ser(concat(1,vector(n+1,k,k^k))))),n)}
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Log( (&+[n^n*x^n: n in [0..m+2]]) ) )); [n*b[n]: n in [1..m-1]]; // _G. C. Greubel_, May 30 2019
%o (Sage) m = 20; T = taylor(log( sum(n^n*x^n for n in (0..m+2)) ), x, 0, m); [n*T.coefficient(x, n) for n in (1..m)] # _G. C. Greubel_, May 30 2019
%Y Cf. A141152, A306628.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Jun 11 2008
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