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Search: id:A030266
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| A030266 |
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Shifts left under COMPOSE transform with itself. |
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+0
24
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| 0, 1, 1, 2, 6, 23, 104, 531, 2982, 18109, 117545, 808764, 5862253, 44553224, 353713232, 2924697019, 25124481690, 223768976093, 2062614190733, 19646231085928, 193102738376890, 1956191484175505, 20401540100814142
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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David Callan, A Combinatorial Interpretation of the Eigensequence for Composition, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.4.
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LINKS
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N. J. A. Sloane, Transforms
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FORMULA
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G.f. A(x) satisfies the functional equation: A(x)-x = x*A(A(x)). - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 04 2002
G.f.: A(x/(1+A(x))) = x. - Paul D. Hanna (pauldhanna(AT)juno.com), Dec 04 2003
Suppose functions A=A(x), B=B(x), C=C(x), etc., satisfy: A = 1 + xAB, B = 1 + xABC, C = 1 + xABCD, D = 1 + xABCDE, etc., then B(x)=A(x*A(x)), C(x)=B(x*A(x)), D(x)=C(x*A(x)), etc., where A(x) = 1 + x*A(x)*A(x*A(x)) and x*A(x) is the g.f. of this sequence (see table A128325). - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 10 2007
G.f. A(x) = x*F(x,1) where F(x,n) satisfies: F(x,n) = F(x,n-1)*(1 + x*F(x,n+1)) for n>0 with F(x,0)=1. - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2007
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PROGRAM
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(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+x*A*subst(A, x, x*A+x*O(x^n))); polcoeff(A, n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 10 2007
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CROSSREFS
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Cf. A001028, A035049.
Cf. A110447.
Cf. A128325.
Sequence in context: A117106 A137534 A137535 this_sequence A110447 A137536 A137537
Adjacent sequences: A030263 A030264 A030265 this_sequence A030267 A030268 A030269
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KEYWORD
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nonn,nice,eigen
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net)
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