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%I #20 May 12 2024 10:04:12
%S 1,2,0,4,-20,36,2296,-71280,1347984,-9104480,-566853584,26068456800,
%T -109901066912,-42816208726368,1570246237628160,105861151925191936,
%U -11551468847311923968,-237265887931262530560,104987271408023239754752,-2079616585958181891671040
%N E.g.f. A(x) satisfies A(A(x)) = x * exp(2*x).
%H Seiichi Manyama, <a href="/A199852/b199852.txt">Table of n, a(n) for n = 1..282</a>
%H Dmitry Kruchinin, Vladimir Kruchinin, <a href="http://arxiv.org/abs/1302.1986">Method for solving an iterative functional equation $A^{2^n}(x)=F(x)$</a>, arXiv:1302.1986
%F a(n)=n!*T(n,1), T(n,m)=if n=m then 1 else 1/2((m^(n-m)*2^(n-m))/(n-m)!-sum(i=m+1..n-1, T(n,i)*T(i,m))).
%e A(x) = x + x^2 + x^4/6 - x^5/6 + x^6/20 + 41*x^7/90 - 99*x^8/56 + ...
%K sign
%O 1,2
%A _Vladimir Kruchinin_, Nov 11 2011
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