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%I #10 Sep 26 2013 03:24:32
%S 1,1,1,101,2301,82601,3287001,149411501,7474902101,406765054801,
%T 23836604715601,1493376284080501,99459838574595501,
%U 7009748111184956601,520845172037612209801,40672220108202107951101,3328819620490715884626501,284871268231239093741932001
%N G.f. A(x) satisfies: A(A(A(A(A(x))))) = G(x) where G(x) = x + 4*x^2 + x*G(G(G(G(G(x))))) is the g.f. of A215118.
%C a(n) == 1 (mod 100).
%e G.f.: A(x) = x + x^2 + x^3 + 101*x^4 + 2301*x^5 + 82601*x^6 + 3287001*x^7 +...
%e Let G(x) = A(A(A(A(A(x))))):
%e G(x) = x + 5*x^2 + 25*x^3 + 625*x^4 + 18125*x^5 + 628125*x^6 + 25390625*x^7 +...
%e such that G(x) = x + 4*x^2 + x*G(G(G(G(G(x))))):
%e G(G(G(G(G(x))))) = x + 25*x^2 + 625*x^3 + 18125*x^4 + 628125*x^5 + 25390625*x^6 +...
%o (PARI) {a(n)=local(A=x+x^2,B=x+4*x^2);for(i=1,n+1,B=x+4*x^2+x*subst(B,x,subst(B,x,subst(B,x,subst(B,x,B+x^2*O(x^n))))));
%o for(j=1, n+1, A=round((4*A+subst(B, x, serreverse(subst(A,x,subst(A,x,subst(A,x,A+x^2*O(x^n)))))))/5));; polcoeff(A, n)}
%o for(n=1, 31, print1(a(n), ", "))
%Y Cf. A215118, A213009, A215115, A215117.
%K nonn
%O 1,4
%A _Paul D. Hanna_, Aug 03 2012
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