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%I
%S 1,1,0,-3,4,50,-264,-1638,25264,40896,-3357360,13380840,559239264,
%T -7126367664,-98536058880,3137828374800,8293939695360,
%U -1427422903584000,10789876955529216,666226173751955712,-14427332604300810240,-279534553922071445760
%N Let f(n)! = n^n. Then f(n) = n g(1/log(n)), where g has the asymptotic series g(x) = Sum a(j) x^j/j!. The given sequence is a(j).
%F E.g.f. A(x), safisfies A(x)=1+x*(A(x))*(1-log(A(x)),
%F a(n)=((n-1)!*sum(i=0..n-1, (binomial(n,i)*sum(j=0..n, j!*(-1)^(j)*binomial(n,j)*stirling1(n-i-1,j)))/(n-i-1)!)), n>0, a(0)=1. [_Vladimir Kruchinin_, Oct 13 2012]
%e f(n) = n (1 + 1/log(n) - 1/(2 log(n)^3) + ...), so a(0) = 1, a(1) = 1, a(2) = 0 and a(3) = (-1/2)*3! = -3.
%o (Maxima)
%o a(n):=if n=0 then 1 else ((n-1)!*sum((binomial(n,i)*sum(j!*(-1)^(j)*binomial(n,j)*stirling1(n-i-1,j),j,0,n))/(n-i-1)!,i,0,n-1)); [_Vladimir Kruchinin_, Oct 13 2012]
%K easy,sign
%O 0,4
%A Jim Ferry (jferry(AT)alum.mit.edu), Mar 14 2003
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