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Search: id:A120566
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| A120566 |
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G.f. satisfies: A(x) = A(A(x)) - x*A(A(A(x))), with A(0)=0. |
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+0
1
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| 1, 1, 1, 3, 7, 33, 109, 643, 2623, 17929, 85349, 652395, 3517911, 29484193, 176844781, 1605009651, 10575269935, 103033059513, 738834271605, 7676696689275, 59466011617671, 655467253898577, 5451048833933693
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OFFSET
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1,4
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FORMULA
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G.f. satisfies: A(-A(-x)) = x ; Also: A(x) = x + A(A(x))*series_reversion(A(x)).
Since g.f. satisfies: A(A(x)) = ( x - A(x) )/A(-x), then higher order self-compositions of A(x) reduce into expressions involving A(x) and A(-x). - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 22 2006
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EXAMPLE
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A(x) = x + x^2 + x^3 + 3x^4 + 7x^5 + 33x^6 + 109x^7 + 643x^8 +...
A(A(x)) = x + 2x^2 + 4x^3 + 12x^4 + 40x^5 + 168x^6 + 736x^7 + 3784x^8+..
x*A(A(A(x))) = x^2 + 3x^3 + 9x^4 + 33x^5 + 135x^6 + 627x^7 + 3141x^8+...
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PROGRAM
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(PARI) {a(n)=local(A=x+x^2+x*O(x^n)); if(n<1, 0, for(i=1, n, A=x-subst(A, x, -x)*subst(A, x, A)); polcoeff(A, n))}
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CROSSREFS
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Sequence in context: A089622 A143967 A007646 this_sequence A057480 A051256 A057795
Adjacent sequences: A120563 A120564 A120565 this_sequence A120567 A120568 A120569
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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), Jun 14 2006
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