%I #15 Oct 09 2017 09:07:05
%S 1,2,-12,216,-5616,186624,-7387200,335736576,-17124804864,
%T 965515500288,-59526188983296,3980690988235776,-286917239797788672,
%U 22174720816561975296,-1829668999418480590848,160570117472696852299776,-14937971163165634577301504,1468791751381133837013319680,-152229793395391092702181785600,16589818156062623434747885780992,-1896733533500219982388526312325120
%N G.f.: A(x) satisfies: A( 4*x - 3*A(x) ) = x - 4*x^2.
%H Vaclav Kotesovec, <a href="/A292812/b292812.txt">Table of n, a(n) for n = 1..330</a> (terms 1..200 from Paul D. Hanna)
%F a(n) ~ (-1)^n * c * 6^n * n! / (n^(1/3) * (log(3))^n), where c = 0.04217549814791850977595... - _Vaclav Kotesovec_, Oct 09 2017
%e G.f.: A(x) = x + 2*x^2 - 12*x^3 + 216*x^4 - 5616*x^5 + 186624*x^6 - 7387200*x^7 + 335736576*x^8 - 17124804864*x^9 + 965515500288*x^10 - 59526188983296*x^11 + 3980690988235776*x^12 - 286917239797788672*x^13 + 22174720816561975296*x^14 - 1829668999418480590848*x^15 +...
%e such that A( 4*x - 3*A(x) ) = x - 4*x^2.
%e RELATED SERIES.
%e Define Ai(x) such that Ai(A(x)) = x, then Ai(x) begins:
%e Ai(x) = x - 2*x^2 + 20*x^3 - 376*x^4 + 9872*x^5 - 325056*x^6 + 12684480*x^7 - 567616512*x^8 + 28519993088*x^9 - 1585862993152*x^10 + 96566543541248*x^11 +...
%e where Ai(x - 4*x^2) = 4*x - 3*A(x).
%o (PARI) {a(n) = my(A=x,V=[1,2]); for(i=1,n, V = concat(V,0); A=x*Ser(V); V[#V] = Vec( subst(A,x, 4*x - 3*A) )[#V]/2 );V[n]}
%o for(n=1,30,print1(a(n),", "))
%Y Cf. A291198, A292813, A292814, A292811, A293454, A293455, A293456.
%K sign
%O 1,2
%A _Paul D. Hanna_, Sep 23 2017
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