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Search: id:A120971
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| A120971 |
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G.f. satisfies: A(x) = 1 + x*A(x)^2*[A(x*A(x)^2)]^2. |
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+0
12
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| 1, 1, 4, 26, 218, 2151, 23854, 289555, 3783568, 52624689, 772928988, 11918181144, 192074926618, 3224153299106, 56213565222834, 1015694652332437, 18982833869517376, 366384235565593176, 7292660345274942402
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OFFSET
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0,3
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FORMULA
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G.f. A(x) satisfies: A(x) = G(G(x)-1), A(G(x)-1) = G(A(x)-1), A(x) = G(x*A(x)^2), and A(x/G(x)^2) = G(x), where G(x) is the g.f. of A120970 and satisfies G(x/G(x)^2) = 1 + x.
G.f. A(x) = F(x,1) where F(x,n) satisfies: F(x,n) = F(x,n-1)*(1 + x*F(x,n+1)^2) for n>0 with F(x,0)=1. - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2007
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EXAMPLE
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Comment from Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2007: G.f. A(x) is the unique solution to variable A in the infinite system of simultaneous equations:
A = 1 + xB^2;
B = A*(1 + xC^2);
C = B*(1 + xD^2);
D = C*(1 + xE^2);
E = D*(1 + xF^2) ; ...
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PROGRAM
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(PARI) {a(n)=local(A, G=[1, 1]); for(i=1, n, G=concat(G, 0); G[ #G]=-Vec(subst(Ser(G), x, x/Ser(G)^2))[ #G]); A=Vec(((Ser(G)-1)/x)^(1/2)); A[n+1]}
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CROSSREFS
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Cf. A120970; variants: A120973, A120975, A120977.
Cf. A002449, A030266, A087949, A088714, A088717, A091713.
Sequence in context: A124554 A048351 A135884 this_sequence A089816 A105616 A107879
Adjacent sequences: A120968 A120969 A120970 this_sequence A120972 A120973 A120974
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 20 2006
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