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%I #22 May 04 2024 06:09:56
%S 0,1,2,0,4,-8,-8,288,-1712,-1888,105472,-288576,-10404800,84940672,
%T 1454871936,-24372060160,-255228956416,8232158755328,49829958005760,
%U -3390379506089984,-7038865141000192,1699612131395493888,-3459036721655810048,-1025681798088053424128
%N G.f. satisfies A(A(A(A(x)))) = F(x), where F(x) is the g.f. for A002697(n) = n*4^(n-1).
%H Seiichi Manyama, <a href="/A372492/b372492.txt">Table of n, a(n) for n = 0..435</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 [math.CO], 2013.
%F Let B(x) = A(A(x)). B(B(x)) = F(x).
%F B(x) = G(2*x)/2, where G(x) is the g.f. for A309509.
%e B(x) = x + 4*x^2 + 8*x^3 + 16*x^4 + 32*x^5 + 256*x^7 + 768*x^8 - 14848*x^9 + 51200*x^10 + ...
%Y Cf. A002697, A309509.
%K sign
%O 0,3
%A _Seiichi Manyama_, May 03 2024