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%I #8 Jul 16 2014 16:01:05
%S 0,1,2,9,72,845,12972,244741,5468176,141111693,4129615540,
%T 135127313101,4888457921688,193733261456605,8346805786382364,
%U 388432439875807125,19417284993350451232,1037672210204182995277,59035412382992193993732
%N E.g.f. satisfies: A(x) = x*(tan(exp(A(x))-1)+1).
%H Alois P. Heinz, <a href="/A133984/b133984.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) ~ n^(n-1) * sqrt(r*s/(r+2*exp(s)*(s-r))) / (exp(n) * r^n), where r = 0.2898872767597687473... and s = 0.5719846912143595905... are roots of the system of equations s+r*tan(1-exp(s)) = r, exp(s)*r = (cos(1-exp(s)))^2. - _Vaclav Kotesovec_, Jul 16 2014
%p A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (tan (exp(A(n-1))-1)+1), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n)*n!: seq (a(n), n=0..22);
%t CoefficientList[InverseSeries[Series[-(x/(-1 + Tan[1 - E^x])),{x,0,20}],x],x] * Range[0,20]! (* _Vaclav Kotesovec_, Jul 16 2014 *)
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 27 2008
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