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%I #5 Aug 27 2013 02:04:03
%S 1,1,-1,1,1,-11,23,-20,731,-4860,-91205,138329,24813133,222203538,
%T -11857627480,-340590475934,7798573417057,602467423292955,
%U -4252676907049394,-1469602631093521547,-14928401886412967891,4982240895059491727005,167923794808862463264206
%N Integer a(n) produces the least positive integer coefficient of x^n in the n-th iteration of g.f. A(x) where A(0)=0.
%e The iterated iterations of g.f. A(x) begin:
%e A(x) = (1)x + x^2 - x^3 + x^4 + x^5 - 11x^6 + 23x^7 - 20x^8 + 731x^9+..
%e A(A(x)) = x + (2)x^2 - 2x^4 + 6x^5 - 8x^6 - 50x^7 + 78x^8 + 1688x^9+...
%e A(A(A(x))) = x + 3x^2 + (3)x^3 - 3x^4 - x^5 + 17x^6 - 81x^7 -370x^8+...
%e A(A(A(A(x)))) = x + 4x^2 + 8x^3 + (4)x^4 - 12x^5 + 4x^6 + 12x^7 +...
%e A(A(A(A(A(x))))) = x + 5x^2 + 15x^3 + 25x^4 + (5)x^5 - 55x^6 -33x^7+...
%e A(A(A(A(A(A(x)))))) = x + 6x^2 + 24x^3 + 66x^4 + 106x^5 + (4)x^6 +...
%e Coefficients [x^n] of n-th self-composition of A(x) forms A119816:
%e [1,2,3,4,5,4,7,8,3,9,11,4,13,11,14,8,17,4,19,4,1,4,23,24,5,17,27,...].
%o (PARI) {a(n)=local(F=x+x^2+sum(k=3,n-1,a(k)*x^k),G=x+x*O(x^n));if(n<1,0,if(n<=2,1, for(k=1,n,G=subst(F,x,G));return((n-polcoeff(G,n,x)) )))}
%Y Cf. A119816, A119817, A112317.
%K sign
%O 1,6
%A _Paul D. Hanna_, May 31 2006
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