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Search: id:A107700
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| A107700 |
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G.f. A(x) satisfies: A(A(x)) = x + 2*A(x)^2. |
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+0
3
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| 1, 1, 1, 0, -2, 0, 13, 0, -145, 0, 2328, 0, -49784, 0, 1358965, 0, -46076544, 0, 1902202515, 0, -94104681660, 0, 5503867176832, 0, -376096374571125, 0, 29714871818774044, 0, -2689473418781240320, 0, 276562260699626541509, 0, -32073434441440654231749, 0
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Inspired by peculiar functional equations suggested by Michael Somos. Unexpectedly, the even-indexed terms are all zeros after index 2; see A107699 for odd-indexed terms. The self-COMPOSE equals A107701.
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FORMULA
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G.f. satisfies: A(-A(-x)) = x.
G.f. satisfies: A( A(x) - 2*x^2 ) = x. [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 20 2008]
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PROGRAM
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(PARI) {a(n)=local(A, B, F); A=x+x^2+x*O(x^n); if(n<1, 0, for(i=0, n, F=x+2*A^2; B=serreverse(A); A=(A+subst(B, x, F))/2); polcoeff(A, n, x))}
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CROSSREFS
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Cf. A107699, A107701.
Sequence in context: A013316 A013310 A058803 this_sequence A122688 A110685 A064855
Adjacent sequences: A107697 A107698 A107699 this_sequence A107701 A107702 A107703
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 21 2005
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