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Search: id:A090594
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| A090594 |
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G.f. satisfies: A(x + x*A(-x)) = x + x*A(x). |
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1
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| 0, 1, 2, 4, 10, 28, 92, 328, 1330, 5740, 27596, 139160, 769964, 4423736, 27567048, 177127440, 1223262698, 8667225836, 65523382052, 506370134232, 4150248267164, 34679055629960, 305773367599064, 2742997917079984, 25853946568986188
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OFFSET
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0,3
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COMMENT
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Series reversion of g.f. A(x) is -A(-x). The g.f. for A006196 (leftist trees with n leaves) also satisfies this condition: A(-A(-x)) = x. This sequence was inspired by communication with Michael Somos, while he was investigating this and similar functional equations and their resulting sequences.
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FORMULA
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G.f.: A(-A(-x)) = x.
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x+x*O(x^n); for(i=1, n, B=subst(A, x, -x); C=subst(A, x, x+x*B); A=A+x+A*x-C); polcoeff(A, n, x))}
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CROSSREFS
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Cf. A006196.
Sequence in context: A149831 A149832 A091175 this_sequence A085549 A022492 A123429
Adjacent sequences: A090591 A090592 A090593 this_sequence A090595 A090596 A090597
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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), Dec 05 2003
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